Cosmogenesis - A Story of Creation in Membrane Mirror Symmetry

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    Cosmogenesis - A Story of Creation in Membrane Mirror Symmetry

    Evolution of Dark Energy as Membrane Curvature and the Mirror Symmetry of a Calabi Yaued Braneworld in a Multitimed Cyclic Cosmology

    History_of_the_Universe_svg.
    http://bicepkeck.org/visuals.html


    0. Abstract and Introduction

    Definiton to Inflaton to Instanton to Continuon - Four Pillars of Creation

    Cosmogenesis I - The Definiton
    Cosmogenesis II - The Inflaton
    Cosmogenesis III - The Instanton
    Cosmogenesis IV - The Continuon


    1. The Definiton
    1.1 The Primary Algorithmic Logos
    1.2 The Secondary Algorithmic Logos
    1.3 The Tertiary Complementary Algorithmic Logos
    1.4 The Modular Duality of Time-Space in the Mathimatia of Supermembrane EpsEss and the Alpha-Variation

    2. The Inflaton
    SEWG-------------SEWg---SEW.G---SeW.G---S.EW.G------S.E.W.G
    Planck Unification I---IIB----HO32-----IIA-----HE64----Bosonic Unification

    2.1 Graviton Unification in Monopole Class IIB
    SEWG ---- SEWg as string transformation from Planck brane to (Grand Unification/GUT) monopole brane
    2.2 Quark-Lepton Unification in XL-Boson Class HO(32)
    SEWg---SEW.G
    2.3 Cosmic Ray Unification in XL-Boson Class IA
    SEW.G --- SeW.G
    2.4 in Quark-Lepton Unification in XL-Boson Class HE(64)
    SeW.G --- S.EW.G

    2.5 The Continuous Inflaton in 10D/4D DeSitter Spacetime

    3. The Instanton
    3.1 Bosonic Unification
    3.2 Baryogenesis without Antimatter
    3.3 The Parametrisation of the Friedmann Equation
    3.4 The Primordial Neutron Decay
    3.5 The first Ylemic Stars in the Universe
    3.6 The Mass Seed Mo in the Planck Plasma Cosmic Friedmann Liquid
    3.7 The wormhole wavelength and the Magnetic Permeability Constant
    3.8 A Synthesis of LCDM with MOND in an Universal Lambda Milgröm Deceleration
    3.9 Newton's Gravitational Constant Measurements

    4. The Continuon
    4.1 The Hubble Node of the Inflaton in the Instanton
    4.2 The Dark Matter - Baryon Matter Intersection
    4.3 The Multiversal Hubble Cycles


    0. Abstract and Introduction:

    The expansion of the universe can be revisited in a reformulation of the standard cosmology model Lambda-Cold-Dark-Matter or LCDM in terms of a parametrization of the standard expansion parameters derived from the Friedmann equation, itself a solution for the Einstein Field Equations (EFE) applied to the universe itself.
    A measured and observed flat universe in de Sitter (dS) 4D-spacetime with curvature k=0, emerges as the result of a topological mirror symmetry between two Calabi Yau manifolds encompassing the de Sitter spacetime in a multitimed connector dimension.
    The resulting multiverse or braneworld so defines a singular universe with varying but interdependent time cyclicities.

    It is proposed, that the multiverse initiates cyclic periods of hyper acceleration or inflation to correlate and reset particular initial and boundary conditions related to a baryonic mass seedling proportional to a closure or Hubble mass to ensure an overall flatness of zero curvature for every such universe parallel in a membrane timespace but colocal in its lower dimensional Minkowski spacetime.

    On completion of a 'matter evolved' Hubble cycle, defined in characteristic Hubble parameters; the older or first universal configuration quantum tunnels from its asymptotic Hubble Event horizon into its new inflaton defined universal configuration bounded by a new Hubble node.
    The multidimensional dynamics of this quantum tunneling derives from the mirror symmetry and topological duality of the 11-dimensional membrane space connecting two Calabi Yau manifolds as the respective Hubble nodes for the first and the second universal configurations.


    Parallel universes synchronise in a quantized protoverse as a function of the original lightpath of the Instanton, following not preceding a common boundary condition, defined as the Inflaton.
    The initial conditions of the Inflaton so change as a function of the imposed cyclicity by the boundary conditions of the paired Calabi Yau mirror duality; where the end of a Instanton cycle assumes the new initial conditions for the next cycle of the Instanton in a sequence of Quantum Big Bangs.

    The outer boundary of the second Calabi Yau manifold forms an open dS spacetime in 12-dimensional brane space (F-Vafa 'bulk' Omnispace) with negative curvature k=-1 and cancels with its inner boundary as a positively curved k=1 spheroidal AdS spacetime in 11 dimensions to form the observed 4D/10-dimensional zero curvature dS spacetime, encompassed by the first Calabi Yau manifold.

    A bounded (sub) 4D/10D dS spacetime then is embedded in a Anti de Sitter (AdS) 11D-spacetime of curvature k=+1 and where 4D dS spacetime is compactified by a 6D Calabi Yau manifold as a 3-torus and parametrized as a 3-sphere or Riemann hypersphere.
    The outer boundary of the 6D Calabi Yau manifold then forms a mirror duality with the inner boundary of the 11D Calabi Yau event horizon.

    Every Inflaton defines three Hubble nodes or timespace mirrors; the first being the 'singularity - wormhole' configuration; the second the nodal boundary for the 4D/10D dS spacetime and the third the dynamic lightpath bound for the Hubble Event horizon in 5D/11D AdS timespace.
    The completion of a 'de Broglie wave matter' evolution cycle triggers the Hubble Event Horizon as the inner boundary of the timespace mirrored Calabi Yau manifold to quantum tunnel onto the outer boundary of the spacetime mirrored Calabi Yau manifold in a second universe; whose inflaton was initiated when the lightpath in the first universe reached its second Hubble node.

    For the first universe, the three nodes are set in timespace as {3.3x10-31 s; 16.88 Gy; 3.96 Ty} and the second universe, timeshifted in t1=to+t with to=1/Ho has a nodal configuration {to+1.4x10-33; to+3,957 Gy; to+972.7 Ty}; the latter emerging from the timespace as the instanton at time marker to.
    A third universe would initiate at a time coordinate t2=to+t1+t as {1/Ho+234.472/Ho +5.8x10-36 s; to+t1+972.7 Ty; to+t1+250,223 Ty}; but as the second node in the second universe cannot be activated by the lightpath until the first universe has reached its 3.96 trillion year marker (and at a time for a supposed 'heat death' of the first universe due to exhaustion of the nuclear matter sources); the third and following nested universes cannot be activated until the first universe reaches its n=1+234.472=235.472 timespace coordinate at 3,974.8 billion years from the time instanton aka the Quantum Big Bang.

    For a present timespace coordinate of npresent=1.13271 however; all information in the first universe is being mirrored by the timespace of the AdS spacetime into the dS spacetime of the second universe at a time frame of t = t1-to = 19.12 - 16.88 = 2.24 billion years and a multidimensional time interval characterizing the apparent acceleration observed and measured in the first universe of the Calabi Yau manifold compressed or compactified flat dS Minkowski cosmology. The solution to the Dark Energy and Dark Matter question of a 'missing mass' cosmology is described in this discourse and rests on the evolution of a multiverse in matter.

    multiverse.


    qtunnel.


    Yn = RHubble/rWeyl = 2πRHubbleWeyl = ωWeyl/Ho = 2πnWeyl = nps/2π = 1.003849x1049

    2nd Inflaton/Quantum Big Bang redefines for k=1: RHubble(1) = n1RHubble = c/Ho(1) = (234.472)RHubble = 3.746x1028 m* in 3.957 Trillion Years for critical nk
    3rd Inflaton/Quantum Big Bang redefines for k=2: RHubble(2) = n1n2RHubble = c/Ho(2) = (234.472)(245.813)RHubble = 9.208x1030 m* in 972.63 Trillion Years for critical nk
    4th Inflaton/Quantum Big Bang redefines for k=3: RHubble(3) = n1n2n3RHubble = c/Ho(3) = (57,636.27)(257.252)RHubble = 2.369x1033 m* in 250.24 Quadrillion Years for critical nk
    5th Inflaton/Quantum Big Bang redefines for k=4: RHubble(4) = n1n2n3n4RHubble = c/Ho(4) = (14,827,044.63)(268.785)RHubble = 6.367x1035 m* in 67.26 Quintillion Years for critical nk
    ...
    (k+1)th Inflaton/Quantum Big Bang redefines for k=k: RHubble(k) = RHubble Π nk = c/Ho Π nk
    .....

    nk = ln{ωWeylRHubble(k)/c}/lnY = ln{ωWeyl/Ho(k)}/lnY


    A general dark energy equation for the kth universe (k=0,1,2,3,...) in terms of the parametrized Milgröm acceleration A(n); comoving recession speed V(n) and scale factored curvature radius R(n):


    Λk (n) = GoMo/Rk(n)2 - 2cHo(Πnk)2/{n-ΣΠnk-1+Πnk)3}

    = {GoMo(n-ΣΠnk-1+Πnk)2/{(Πnk)2.RH2(n-ΣΠnk-1)2} - 2cHo(Πnk)2/{n-ΣΠnk-1+Πnk)3}

    Λo = GoMo(n+1)2/RH2(n)2 - 2cHo/(n+1)3
    Λ1 = GoMo(n-1+n1)2/n12RH2(n-1)2 - 2cHon12/(n-1+n1)3
    Λ2 = GoMo(n-1-n1+n1n2)2/n12n22RH2(n-1-n1)2 - 2cHon12n22/(n-1-n1+n1n2)3
    .....

    Lambda-DE-Quintessence Derivatives:

    Λk'(n) = d{Λk}/dn =
    {GoMo/Πnk2RH2}{2(n-ΣΠnk-1+Πnk).(n-ΣΠnk-1)2 - 2(n-ΣΠnk-1).(n-ΣΠnk-1+Πnk)2}/{(n-ΣΠnk-1)4} - {-6cHo(Πnk)2}/(n-ΣΠnk-1+Πnk)4

    = {-2GoMo/ΠnkRH2}(n-ΣΠnk-1+Πnk)/(n-ΣΠnk-1)3 + {6cHo(Πnk)2}/(n-ΣΠnk-1+Πnk)4

    = {6cHo(1)2}/{(n-0+1)4} - {2GoMo/1.RH2}{(n-0+1)/(n-0)3}........................................ for k=0
    = {6cHo(1.n1)2}/{(n-1+n1)4} - {2GoMo/n1.RH2}{(n-1+n1)/(n-1)3}................................ for k=1
    = {6cHo(1.n1.n2)2}/{(n-1-n1+n1.n2)4} - {2GoMo/n1n2.RH2}{(n-1-n1+n1n2)/(n-1-n1)3}...... for k=2
    .......

    For k=0; {GoMo/3c2RH} = constant = n3/[n+1]5
    for roots nΛmin = 0.23890175.. and nΛmax = 11.97186...
    {GoMo/2c2RH} = constant = [n]2/[n+1]5
    for Λo-DE roots: n+/- = 0.1082331... and n-/+ = 3.40055... for asymptote Λ0∞ = GoMo/RH2 = 7.894940128...x10-12 (m/s2)*

    For k=1; {GoMo/3n13c2RH} = constant = [n-1]3/[n-1+n1]5 = [n-1]3/[n+233.472]5
    for roots nΛmin = 7.66028... and nΛmax = 51,941.9..
    {GoMo/2n14c2RH} = constant = [n-1]2/[n-1+n1]5 = [n-1]2/[n+233.472]5
    for Λ1-DE roots: n+/- = 2.29966... and n-/+ = 7,161.518... for asymptote Λ1∞ = GoMo/n12RH2 = 1.43604108...x10-16 (m/s2)*


    For k=2; {GoMo/3n13n23c2RH} = constant = [n-1-n1]3/[n-1-n1+n1n2]5 = [n-235.472]3/[n+57,400.794]5
    for roots nΛmin = 486.7205 and nΛmax = 2.0230105x108
    {GoMo/2n14n24c2RH} = constant = [n-1-n1]2/[n-1-n1+n1n2]5 = [n-235.472]2/[n+57,400.794]5
    for Λ2-DE roots: n+/- = 255.5865... and n-/+ = 1.15383...x107 for asymptote Λ2∞ = GoMo/n12n22RH2 = 2.3766059...x10-21 (m/s2)*




    and where

    Πnk=1=no and Πnk-1=0 for k=0
    with Instanton/Inflaton resetting for initial boundary parameters

    Λo/adeBroglie = GoMo/Rk(n)2/ΠnkRHfps2
    = {GoMo(n-ΣΠnk-1+Πnk)2/{[Πnk]2.RH2(n-ΣΠnk-1)2(ΠnkRHfps2)} = (Πnk)½Ωo

    for Instanton-Inflaton Baryon Seed Constant Ωo = Mo*/MH* = 0.02803 for the kth universal matter evolution

    k=0 for Reset n=nps=Hot and Λo/adeBroglie = GoMo(nps+1)2/{RH3nps2(fps2)} = GoMo/RHc2 = Mo/2MH = ½Ωo
    k=1 for Reset n=1+nps and Λo/adeBroglie = GoMo(1+nps-1+n1)2/{[n1]2.RH3(1+nps-1)2(n1fps2)} = Mo/2n1MH = Mo/2MH* = ½Ωo*
    k=2 for Reset n=n1+1+nps and Λo/adeBroglie = GoMo(n1+1+nps-1-n1+n1n2)2/{[n1n2]2.RH3(n1+1+nps-1-n1)2(n1n2fps2)} = ½Ωo**
    k=3 for Reset n=n1n2+n1+1+nps and Λo/adeBroglie = GoMo(n1n2+n1+1+nps-1-n1-n1n2+n1n2n3)2/{[n1n2n3]2.RH3(n1n2+n1+1+nps-1-n1-n1n2)2(n1n2n3fps2)} = ½Ωo***
    ......

    with nps = 2πΠnk-1.Xnkps/RH = Hotps = Ho/fps = ctps/RH and RH=2GoMH/c2

    No=Hoto/no=Hot=n
    N1=Hot1/n1=(n-1)/n1
    N2=Hot2/n1n2=(n-1-n1)/n1n2
    N3=Hot3/n1n2n3=(n-1-n1-n1n2)/n1n2n3
    ....
    dn/dt=Ho
    .....

    Nk=Hotk/Πnk=(n-ΣΠnk-1)/Πnk
    tk = t - (1/Ho)ΣΠnk-1 for no=1 and No=n

    to=t=n/Ho=No/Ho=nRH/c
    t1=t-1/Ho=(n-1)/Ho=[n1N1]/Ho
    t2=t-(1+n1)/Ho=(n-1-n1)/Ho=(n1n2N2)/Ho
    t3=t-(1+n1+n1n2)/Ho=(n-1-n1-n1n2)/Ho=(n1n2n3N3)/Ho
    .......

    R(n)=R(No)=noRH{n/[n+1]}=RH{n/[n+1]}
    R1(N1)=n1RH{N1/[N1+1]}=n1RH{[n-1]/[n-1+n1]}
    R2(N2)=n1n2RH{N2/[N2+1]}=n1n2RH{[n-1-n1]/[n-1-n1+n1n2]}
    R3(N3)=n1n2n3RH{N3/[N3+1]}=n1n2n3RH{[n-1-n1-n1n2]/[n-1-n1-n1n2+n1n2n3]}
    .......


    Rk(n) = ΠnkRH(n-ΣΠnk-1)/{n-ΣΠnk-1+Πnk}

    .....= RH(n/[n+1]) = n1RH(N1/[N1+1]) = n1n2RH(N2/[N2+1]) =.....



    Vk(n) = dRk(n)/dt = c{Πnk}2/{n-ΣΠnk-1+Πnk}2

    .....= c/[n+1]2 = c/[N1+1]2 = c/[N2+1]2 =.....
    .....= c/[n+1]2 = c(n1)2/[n-1+n1]2 = c(n1n2)2/[n-1-n1+n12n22]2 =.....



    Ak(n) = d2Rk(n)/dt2 = -2cHo(Πnk)2/(n-ΣΠnk-1+Πnk)3

    .....= -2cHo/(n+1)3 = -2cHo/n1(N1+1)3 = -2cHo/n1n2(N2+1)3=.....
    ..... = -2cHo/[n+1]3 = -2cHo{n1}2/[n-1+n1]3 = -2cHo(n1n2)2/[n-1-n1+n1n2]3 =.....

    GoMo is the Gravitational Parameter for the Baryon mass seed; Curvature Radius RH = c/Ho in the nodal Hubble parameter Ho and c is the speed of light



    The Friedmann's acceleration equation and its form for the Hubble time derivative from the Hubble expansion equation substitutes a curvature k=1 and a potential cosmological constant term; absorbing the curvature term and the cosmological constant term, which can however be set to zero if the resulting formulation incorporates a natural pressure term applicable to all times in the evolvement of the cosmology.


    Deriving the Instanton of the 4D-dS Einstein cosmology for the Quantum Big Bang (QBB) from the initial-boundary conditions of the de Broglie matterwave hyper expansion of the Inflaton in 11D AdS then enables a cosmic evolution for those boundary parameters in cycle time n=Hot for a nodal 'Hubble Constant' Ho=dn/dt as a function for a time dependent expansion parameter H(n)=Ho/T(n)=Ho/T(Hot).

    It is found, that the Dark Matter (DM) component of the universe evolves as a function of a density parameter for the coupling between the inflaton of AdS and the instanton of dS space times. It then is the coupling strength between the inflationary AdS brane epoch and the QBB dS boundary condition, which determines the time evolution of the Dark Energy (DE).
    Parametrization of the expansion parameter H(n) then allows the cosmological constant term in the Friedmann equation to be merged with the scalar curvature term to effectively set an intrinsic density parameter at time instantenuity equal to Λ(n) for ΛpsQBB=GoMo/λps2 and where the wavelength of the de Broglie matter wave of the inflaton λps decouples as the Quantum Field Energy of the Planck Boson String in AdS and manifests as the measured mass density of the universe in the flatness of 4D Minkowski spacetime.


    dH/dt + 4πGρ = - 4πGP/c2

    ... (for V4/10D=[4π/3]RH3 and V5/11D=2π2RH3 in factor 3π/2)

    For Hypersphere Volumar of 3-sphere: d2{V4}/dR2 = d2{½π2R4}/dR2 = d{2π2R3}/dR = 6π2R2
    Surface Area of Horn Torus (2πR)(2πR)= 4π2R2

    Linearisation of λps = 2πrps = npsRH = c/fps = HoRH/fps

    4πMo/R3 = Mo/{2π2ps/2π)3} = Mo/{4π2ps/2π}3 for Eps -ZPE/VPE density 4πEps/rps3

    {4πMo/R3}.{3π/2} = 3Mo/{4π(λps/2π)3} = 6π2Mops3 = 4π.{3π/2}Mops3 = 4πFeigenbaum chaos limit {Mops3}


    areset = Rk(n)AdS/Rk(n)dS + ½ = n-ΣΠnk-1+Πnk
    Scalefactor modulation at Nk = {[n-ΣΠnk-1]/Πnk } = ½ reset coordinate

    {dH/dt} = areset .d{Ho/T(n)}/dt = - Ho2(2n+1)(n+3/2)/T(n)2 for k=0

    dH/dt + 4πGρ = - 4πGP/c2

    -Ho2(2n+1)(n+3/2)/T(n)2 + GoMo/{RH3(n/[n+1])3}{4p} = Λ(n)/{RH(n/[n+1])} + Λ/3
    -2Ho2{[n+1]2-¼}/T[n]2 + GoMo/RH3(n/[n+1])3{4p} = Λ(n)/RH(n/[n+1]) + Λ/3
    -2Ho2{[n+1]2-¼}/T(n)2 + 4p.GoMo/RH3(n/[n+1])3 = Λ(n)/RH(n/[n+1]) + Λ/3

    For a scalefactor a=n/[n+1] = {1-1/[n+1]} = 1/{1+1/n}

    Λ(n)/RH(n/[n+1]) = - 4πGP/c2 = GoMo/RH3(n/[n+1])3 -2Ho2/(n[n+1]2)

    and Λ = 0
    for -P(n) = Λ(n)c2[n+1]/4πGonRH = Λ(n)Hoc[n+1]/4πGon = Moc2[n+1]3/4πn3RH3 - Ho2c2/2πGon[n+1]2

    For n=1.13271:............ - (+6.696373x10-11 J/m3)* = (2.126056x10-11 J/m3)* + (-8.8224295x10-11 J/m3)*
    Negative Dark Energy Pressure = Positive Matter Energy + Negative Inherent Milgröm Deceleration(cHo/Go)​


    The Dark Energy and the 'Cosmological Constant' exhibiting the nature of an intrinsic negative pressure in the cosmology become defined in the overall critical deceleration and density parameters. The pressure term in the Friedmann equations being a quintessence of function n and changing sign from positive to negative to positive as indicated.
    For a present measured deceleration parameter qdS=-0.5586, the DE Lambda calculates as -6.696x10-11 (N/m2=J/m3)*, albeit as a positive pressure within the negative quintessence.

    In the early radiation dominated cosmology; the quintessence was positive and the matter energy dominated the intrinsic Milgröm deceleration from the Instanton n=nps to n=0.18023 (about 3.04 Billion years) when the quintessence vanished and including a Recombination epoch when the hitherto opaque universe became transparent in the formation of the first hydrogen atoms from the quark-lepton plasma transmuted from the X-L Boson string class HO(32) of the Inflaton epoch preceding the Quantum Big Bang aka the Instanton.

    From the modular membrane duality for wormhole radius rps = λps/2π, the critical modulated Schwarzschild radius rss = 2πλss = 2πx1022 m* for λps = 1/λss
    and for an applied scalefactor a = n/[n+1] =λss/RH = {1-1/[n+1]}

    for a n=Hot coordinate nrecombination = 6.259485x10-5 or about 6.259485x10-5(16.88 Gy) = 1.056601 Million years
    attenuated by exp{-hf/kT} = e-1 = 0.367879 to a characteristic cosmological time coordinate of 0.36788x1.056601 = 388,702 years after the Instanton nps.

    The attenuation of the recombination coordinate then gives the cosmic temperature background for this epoch in the coordinate interval for the curvature radius
    R(n=2.302736x10-5) = 3.67894x1021 m* to R(n=6.259485x10-5) = 1022 m*.
    This radial displacement scale represents the size of a typical major galaxy in the cosmology; a galactic structure, which became potentialised in the Schwarzschild matter evolution and its manifestation in the ylemic prototypical first generation magnetar-neutron stars, whose emergence was solely dependent on the experienced cosmic temperature background and not on their mass distributions.

    The temperature evolution of the Instanton can be written as a function of the luminosity L(n,T) with R(n)=RH(n/[n+1]) as the radius of the luminating surface
    L(nps,T(nps) = 6π2λps2.σ.Tnps4 = 2.6711043034x1096 Watts*, where σ = Stefan's Constant = 2π5k4/15h3c2 and as a product of the defined 'master constants' k, h, c2, π and 'e'.

    L(n,T) = 3HoMo.c2/550n and for Temperature T(nps) ----------- T(nps) = 2.93515511x1036 Kelvin*.

    T(n)4 = HoMoc2/(2π2σRH2[550n3/[n+1]2]) for
    T(n)4 = {[n+1]2/n3}HoMoc2/(2π2σRH2[550]) = 18.1995{[n+1]2/n3} (K4/V)*
    for a temperature interval in using the recombination epoch coordinates T(n1=6.2302736x10-5) = 2945.42 K* to T(n2=6.259485x10-5) = 2935.11 K*

    decepar.
    friedmann2.
    CurvatureAdS.

    relativity032.



    Inflation Curvature, Waved Matter and Hypermass

    Describing the Einstein Lambda in the form of a parametrized Curvature Radius Λ(n)/RHubble= Λ(n)Ho/c = Λ(n)/RH in AdS then enables the scale of the classically geometric Einstein Lambda in squared Hubble units to unitize the quantum geometric Planck-brane-string units by modular mirror duality between the curvature 1/R(n)2 and its radius R(n) with the gravitational parameter G(n)(M(n) modulating the mass M in its Schwarzschilded 'eternal' form to the energy content in the universe by E=mc2.

    As the magnitude of the Einstein Lambda of the instanton is of the order of 2x1085 acceleration units and relates to the baryonic matter (BM) density in the seedling mass Mo/2M =½ΩBMps; with 'closure' mass M=RH.c2/2Go=c3/2GoHo relates to the wormhole mass mps=hfps/c2 =2.222..x10-20 kg; as quantum eigenstate; the coupling between the Planck density ρP=lP3/mP=1.85x1096 and the 'critical closure' density ρH=M/RH3 becomes subject to the overall mass evolution from the wormhole mass to the 'closure mass' over the evolution cycle, ending after for nreset=234.5 for 3.96 Trillion years.

    The coupling between the Planck Density and the Inflaton-Instanton Density so is: mps/RH3 = hfpsc4/8Go3MH3 = 5.45x10-99 .

    A modular brane mirror-T duality between the inversion properties of two parts of a heterotic supermembrane (class HE(8x8)) and can be expressed in the unitary dimensions of the Gravitational Constant Go in [m3][kg-1][s-2]=(Volume)(Angular Acceleration)/(Mass)=(Angular Acceleration)/(Density).


    Brane mirror duality unifies the electromagnetic and gravitational interactions via the coupling of their fine structures.
    The quantization of mass m so indicates the coupling of the Planck Law in the frequency parameter to the Einstein law in the mass parameter.
    The postulative basis of M-Theory utilizes the coupling of two energy-momentum eigenstates in the form of the modular duality between so termed 'vibratory' (high energy and short wavelengths) and 'winding' (low energy and long wavelengths) self-states.

    The 'vibratory' self state is denoted in: Eps=Eprimary sourcesink=hfps=mpsc2 and the 'winding' and coupled self state is denoted by: Ess=Esecondary sinksource=hfss=mssc2

    The F-Space Unitary symmetry condition becomes: fpsfss=rpsrss=(λps/2π)(2πλss)=1

    The coupling constants between the two eigenstates are so: EpsEss=h2 and Eps/Ess=fps2=1/fss2
    The Super-membrane EpsEss then denotes the coupled superstrings in their 'vibratory' high energy and 'winded' low energy self states.

    The coupling constant for the vibratory high energy describes a MAXIMISED frequency differential over time in df/dt|max=fps2 and the coupling constant for the winded low energy describes its MINIMISED reciprocal in df/dt|min=fss2.

    F-Theory also crystallizes the following string formulations from the EpsEss superbrane parameters.


    Electromagnetic Fine structure: αe = 2πke2/hc = e2/2ε0hc

    Gravitational Fine structure (Electron): αg = 2πGome2/hc = {me/mPlanck}2

    Gravitational Fine structure (Primordial Nucleon): αn = 2πGomc2/hc

    Gravitational Fine structure (Planck Boson): αPlanck = 2πGomPlanck2/hc


    1/Eps=e*=2Rec2=√{4αhce2/2πGome2}=2e√α[mP/me=2e√{αeg} = {2e2/me}√(k/Go)=2e2/Gome = e2/2πεome
    for Go = 1/k = 4πεo for the cosmological unification of the fine structures.


    Eps = 1/Ess = 1/e* = ge}/2e = Gome/2e2

    Here e* is defined as the inverse of the sourcesink vibratory superstring energy quantum Eps=E* and becomes a New Physical Measurement Unit is the StarCoulomb (C*) and as the physical measurement unit for 'Physical Consciousness'.

    Re is the 'classical electron radius' coupling the 'point electron' of Quantum- Electro-Dynamics (QED) to Quantum Field Theory (QFT) and given in the electric potential energy of Coulomb's Law in: mec2=ke2/Re; and for the electronic restmass me.
    Alpha α is the electromagnetic finestructure coupling constant α=2πke2/hc for the electric charge quantum e, Planck's constant h and lightspeed constant c.
    Go is the Newtonian gravitational constant as applicable in the Planck-Mass mP=√(hc/2πGo).

    Alternatively expressed, the mass seedling Mo of the QBB manifests in an emerging 'Black Hole' evolution and is bounded by the 'closure' mass M=MHubble. There so must be an energy gradient between the Hubble mass and the seedling mass in direct proportion to the de Broglie inflaton/instanton event.

    The universe begins with a baryon matter seed of 2.813% in AdS spacetime, which allows the emergence of a first generation family of 'eternal' Black Holes to seed 'eternal' White Holes manifesting as quasars which seed galaxies from a first generation of protostars as a function of temperature and independent of mass. Those 'ylem' stars can be shown to be naturally degenerate 'proto' magnetars and neutron stars, whose gravitational inward pressure is balanced by their thermal heat content deriving from the Cosmic radiation temperature.

    The general Jeans formulation for ylem stars is Rylem = √{kTRe3/Gomc2}, Re=e2/4πεomec2 and mc is a prototypical nucleon mass.

    The Dark Energy Interaction Goldstone Gauge Boson is the Graviton manifesting from its 11/5D AdS membrane space Dirichlet 'open string' attachment from AdS spacetime into dS spacetime.



    " Spacetime tells matter how to move; matter tells spacetime how to curve."


    Wheeler's succinct summary of Einstein's theory of general relativity, in Geons, Black Holes, and Quantum Foam, p. 235. - 1998 by John Archibald Wheeler and Kenneth Ford; W.W.Norton and Company; New York, London


    The quote of John Archibald Wheeler can be extended in a question.

    "Is the presence of matter required for spacetime to curve or is the presence of spacetime sufficient for a matter dynamic to emerge and to eventuate?"

    wheeler-.37155.


    The Birth of Space and Time with Spacetime Inflation Curvature preceding Big Banged Wormhole Matter

    The problem of the singularity regarding the creation event, known as the Quantum Big Bang in General Relativity is well addressed in the literature of science and an appropriate solution to the infinite continuous regression of spacetime parameters is resolved in a disengagement and an unnecessity of and for a prior existing spacetime background for matter to act within.
    It is the nature of the string itself, which in particular initial- and boundary conditions allows the concepts of space and time to emerge from the qualitative and quantitative nature of the string definition itself.

    In particular a discretization of dynamical parameters of an describing cosmology in defined Planckian parameters serves to replace the infinite mathematical pointlike singularity to a so called Plancking string vibration formulated as the Planck length lPlanck and which can be considered to be a mimimum displacement as a wormhole radius.
    Any displacement scale below the Planck length then is rendered unphysical and so becomes mathematically inapplicable to describe the dynamics in a physical universe, described by a cosmology, which defines a string epoch characterized by a cosmological inflationary Inflaton from a defined Planck-Length-Quantum-Oscillation/Fluctuation to a so labeled Quantum Big Bang Instanton.

    The Big Bang Instanton becomes defined in a final manifestation of the Planckian Supermembrane (Class I at Planck Time) from the Inflaton to the Instanton (Class HE 8x8 at Weyl-Wormhole Time) and transforming the string energies across string classes from I to IIB, HO 32 and IIA to HE 8x8.

    The Inflaton defined a 11-dimensional supermembraned de Sitter closed - and positively curved cosmology with a defined Hubble Event horizon for a positive spheroidal curvature information bound.
    This closed universe contained no matter seed, but was defined in its curvature through a unification condition relating the electromagnetic finestructure alpha {a=2pke2/hc} to the gravitational finestructure omega {ω = 2πGomPlanck2/hc} via ke2 = e2/4πεo = GoMunification2 for e2 = {Go/k}Munification2
    requiring dimensional mensuration identity in inflaton space [C2/Jm]=[Farad/meter] = [Jm/kg2] for [C] = [C*] = [StarCharge Coulomb] = [m3/s2] = [VolumexAngular Acceleration] and for the Maxwell Constant 1/c2 = μoo = {120π/c}{1/120πc} and 'Free Space' Inflaton Impedance Zo= electric field strength E/magnetic field strength H = √(μoo) = cμo = 1/cεo = 120π}.

    Therefore,
    [Go]mod =[4πεo]mod = [1/k]mod and the inflaton dimensionless string modular unity is Gok=1 for e2 = Go2.Munification2 = Munification2/k2 and Munification = 30[ec] that is 30 modulated magnetic monopole masses. It is this 30[ec]modular inflaton mass, which represents the initial breaking of the inherent supersymmetry of the Planck superstring class I at the Planck energy level to the monopole superstring energy of superstring class IIB with the Planck mass being replaced by 30 monopole masses as the integration of 30 [ec] monopole masses at the [ec3]mod = 2.7x1016 GeV energy level of the Grand Unification Energy separating the quantum gravity from the GUT symbolized as SEW.G.

    Setting ω=1 defines the Planck-Mass and setting a proto-nucleon seed mc=mPlanck9 allows the breaking of the inflaton supersymmetry in the superstring classes.
    Replacing the protonucleon mass mc = √{hc/2πGo}.{60πe2/h}9 = 9.924724523x 10-28 kg by the effective electron mass me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg sets the Electromagnetic Interaction/Gravitational Interaction ratio EMI/GI = e2/Go2me2 = {e/Gome}2 = 2.421821677x1042 using string units.



    The Instanton following the Inflaton then defines a 10-dimensional superstringed Anti de Sitter open - and negatively hyperbolically curved cosmology, bounded in the 11-dimensional asymptotic Hubble Event Horizon.


    hayes-.37157.



    Modular String Duality and the Wormhole Curvature Boundary

    The concept of modular (Mirror/T) duality in supermembrane theory relates a maximum or large spacial displacement radius R as a low frequency and low energy named as a 'winding mode' to its inverse minimum or small spacial displacement radius 1/R as a high frequency and high energy as a 'vibratory mode'.
    The utility of either 'string mode' would then result in an identical physical description either using a 'macroquantum' radius R or a 'microquantum' radius 1/R.

    c = λmin.fmax = 2πRmin.fmax as lightspeed invariance for the vibratory string mode Rcurvature = Rmin = λmin /2π = Wormhole Perimeter/2π

    1/c = 1/(λmin.fmax) = λmax.fmin = λmax/fmax = Rmax.fmin/2π as lightspeed invariance for the winding string mode Rcurvature = Rmax = 2π.λmax = 2π/Wormhole Perimeter

    For the Harmonic Planck Energy Oscillator Energy Eo = ½hfo = ½moc2 = ½kTPlanck


    Planck Mass = mPlanck = √{hc/2πGo}
    Planck Energy = EPlanck = mPlanck.c2 = √{hc5/2πGo} = hfPlanck = hc/lPlanck = kTPlanck
    Planck Length =lPlanck = λPlanck/2π = √{hGo/2πc3}
    Planck Temperature = TPlanck = EPlanck/k = √{hc5/2πk2Go}
    Planck Density = ρPlanck= mPlanck/VPlanck = √{4π2c10/h2Go4}/2π2 = c5/πhGo2= 9.40x1094 kg/m3 for 9x1060 permutation vibratory string eigenstates by |fps2|mod.

    Energy Density Inflaton/Energy Density Instanton = EPlanck.VBigBang/EBigBangVPlanck with minimum Inflaton Planck Oscillator: EoPlanck = ½mPlanckc2
    = mPlanck.rwormhole3/mwormhole.lPlanck3 = √{(hc/2πGo)(2πc3/hGo)}(2πc3/hGo)(rwormhole3/mwormhole} = (c2/Go)(2πc3/hGo){rwormhole3/mwormhole}
    = (2πc5/hGo2){rwormhole3/mwormhole} = {4π2k2/h2Go} (hc5/2πGok2){rwormhole3/mwormhole} = {kTPlanck}2(2πrwormhole)2{1/h2Go}{rwormhole/mwormhole}
    = {EPlanck}2.{c/hfwormhole}2.{1/Go}}{rwormhole/mwormhole} = {EPlanck/EBigBang}2.{rwormhole}{c2/Gomwormhole} for the minimum Instanton Planck Oscillator: EoPlanck = ½mwormholec2

    VBigBang/VPlanck = {EPlanck/EBigBang}.{rwormhole}{c2/Gomwormhole} for EVBigBang/EVPlanck = EVInstanton/EVInflaton = rwormhole/Rowormhole = NAvagadro-Instanton and counting the amount of wormhole string transformed from the Inflaton as the Instanton of the Quantum Big Bang and as the constant 5.801197676..x1023 in string units.





    The Coupling of the Energy Laws by the Self-Frequency of the Quantum for Mass

    It has been discovered, that the universe contains an intrinsic coupling-parameter between its inertial masscontent and its noninertial energy content.
    The matter in the universe is described by the physical parameter termed Mass (M), say as proportional to Energy (E) in Einstein's famous equation Mass M=E/c2.
    This mass M then reappears in Newtonian mechanics as the change in momentum (p) defining the Inertial Mass (Mi) as being proportional to some applied Force (F) or the 'work done' for a particular displacement {F=dp/dt for p=mv and v a kinetematic velocity as the ratio of displacement over time generalised in the lightpath X=cT}.

    It is also well understood, that the inertial mass Mi has a gravitational counterpart described not by the change in momentum of inertia carrying matter agglomerations; but by the geometric curvature of space containing matter conglomerations. This Gravitational Mass Mg is measured to be equivalent to the Inertial Mass Mi and is formulated in the 'Principle of Equivalence' in Einstein's Theory of General Relativity.
    F-Theory then has shown, that this Inertial Mass Mi is coupled inherently to a 'mass-eigen' frequency via the following formulation:

    (1) Energy E=hf=mc2 (The Combined Planck-Einstein Law)
    (2) E=hf iff m=0 (The Planckian Quantum Law E=hf for lightspeed invariance c=λf)
    (3) E=mc2 iff f=fo=fss (The Einstein Law E=mc2 for the lightspeed upper limit)

    (1) Whenever there is mass (M=Mi=Mg) occupying space; this mass can be assigned either as a photonic mass {by the Energy-Momentum relation of Special Relativity: E2=Eo2+(pc)2} by the photonic momentum p=h/λ=hf/c} OR a 'restmass' mo=m/√[1-(v/c)2] for 'restenergy' Eo=moc2.

    The 'total' energy for the occupied space so contains a 'variable' mass in the 'combined' law; but allows particularisation for electromagnetic radiation (always moving at the Maxwell lightspeed constant c in Planck's Law and for the 'Newtonian' mass M in the Einstein Law.

    (2) If M=0, then the Einstein Law is suppressed in favour of the Planck Law and the space contained energy E is photonic, i.e. electromagnetic, always dynamically described by the constancy of lightspeed c.

    (3) If M>0, then there exists a mass-eigen frequency fss=fo=Ess/h=mssc2/h, which QUANTIZES all mass agglomerations m=Σmss in the massquantum mss=Ess/c2.



    The Wave Matter of de Broglie: λdeBroglie = h/p



    The Wavematter of de Broglie from the Energy-Momentum Relation is applied in a (a) nonrelativistic, a (b) relativistic and a (c) superluminal form
    in the matter wavelength: λdeBroglie = h/p = hc/pc for (pc) = √{E2 - Eo2}= moc2.√{[v/c]2/(1-[v/c]2)}

    (a) Example:
    A pellet of 10g moves at 10 m/s for a de Broglie wavelength vdB = h/mv = h/0.1 = 6.7x10-33 m*
    This matter wavelength requires diffraction interference pattern of the order of ldB to be observable and subject to measurement


    (b) Example:
    An electron, moving at 80% of light speed 'c' requires relativistic development

    Eo = moc2 with E = mc2 = moc2/√{1-[v/c]2}, a 66.66% increase in the electron's energy describing the Kinetic Energy E - Eo = {m - mo}c2
    for a relativistic momentum p = moc.√{[0.8]2/(1-[0.8]2)} = (1.333..) moc = h/λdeBroglie and for a relativistic de Broglie wavelength, 60% smaller, than for the nonrelativistic electron in
    λdeBroglie = h/1.333..moc < h/0.8moc =λdeBroglie (1.83x10-12 m relativistic and 3.05x10-12 m* non-relativistic for an electron 'restmass' of 9.11x10-31 kg* and measurable in diffraction interference patterns with apertures comparable to this wavematter scale)


    (c) The de Broglie matter wavespeed in its 'group integrated' form derives from the postulates of Special Relativity and is defined in the invariance of light speed 'c' as a classical upper boundary for the acceleration of any mass M.
    In its 'phase-individuated' form, the de Broglie matter wave is 'hyperaccelerated' or tachyonic, the de Broglie wave speed being lower bounded by light speed 'c'

    vphase = wavelength.frequency = (h/mvgroup)(mc2/h) = c2/vgroup > c for all vgroup < c

    m = Energy/c2 = hf/c2 = hc/λdeBrogliec2 = h/λdeBrogliec = mdeBroglie = [Action as Charge2]mod/c(Planck-Length Oscillation)
    = [e2]mod/clPlanck√alpha = [e2c2/ce]mod = [ec]modular

    as monopole mass of GUT-string IIB and as string displacement current mass equivalent for the classical electron displacement 2Re = e*/c2 = [ec]modular as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy quantum Eps=hfps=mpsc2=kTps
    as a function of e*=1/Eps of Heterotic superstring class HE 8x8
    and relating the Classical Electron Diameter {2Re} as Monopole Mass [ec]mod in Curvature Radius rpsps/2π = Gomps/c2

    The factor 2Go/c2 multiplied by the factor 4π becomes Einstein's Constant k = 8πGo/c2 = 3.102776531x10-26 m/kg describing how spacetime curvature relates to the mass embedded in that spacetime in the theory of General Relativity.

    The selfduality of the superstring IIB aka the Magnetic Monopole selfstate in GUT Unification 2Re/30[ec]mod = 2Rec2/30[ec3]mod = e*/30[ec3]modκ
    for a proportionality constant
    {κ*}=2Re/30k[ec]mod = 2Re.c2/8πe = e*/8πe =1.2384..x1020 kg*/m* in string units for StarCharge in Star Colomb C*/ElectroCharge in Coulomb C unified.

    The monopolar Grand Unification (SEWG gravitational decoupling SEW.G) has a Planck string energy reduced at the IIB string level of
    e*=[ec3]modular for mpsc2c/[ec]modular = [c3]modular = 2.7x1025 electron volt or 4.3362x106 J for a monopole mass [ec]modular = mmonopole = 4.818x10-11 kg* .

    Mass M = n.mss = Σmss = n.{h/2πrdeBrogliec} .[Ess.e*]mod = n.mps.[Ess.{9x1060}.2π2Rrmp3]mod = n.mps.[Ess.{2Re.c2}]mod = n.[Eps.Ess]mod.[2Re]mod
    for λdeBroglieps=h/mpsc and [Eps.e*]mod =1

    {2Rec2} = 4GoMHyper for the classical electron radius Re=ke2/mec2 and describes its HyperMass MHyper-electron = Rec2/2Go = ke2/2Gome = 1.125x1012 kg* for an effective electron mass of me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg* in string units and where k=1/4πεo = 9x109 (Nm2/C2)*.

    The curvature radius for the electron mass me = relectronc2/2Go then becomes relectron = 2Gome/c2 = 2.293957...x10-57 m* in string-membrane inflaton space as 1.44133588x10-34 rps in the wormhole instanton space.

    Re/rinflaton-electron = MHyper-electron/me = 1.2109108..x1042 = ½(EMI/GI) = ½(e2/Go2me2) =½ {e/Gome}2 = ½(2.421821677x1042 ) for the classical electron radius Re halved from the classical electron diameter 2Re from the definition for the modulated supermembrane coupled in EpsEss=h2 and Eps/Ess=fps2=1/fss2.

    Mass M = n.mss = Σmss = n.{mps} .[Ess.e*]mod = n.{mps}[{hfss}{fps/fss}.2π2Rrmp3]mod = n.mps.[Eps.e*/fss2]mod = n.mps/|fss2|mod



    HyperMass and the Hawking Modulus in Curvature of Spacetime

    A general solution for the Curvature Radius RCurvature embedded in a spacetime and as a static boundary condition for a Black Hole is given as the Schwarzschild metric from the field equations of General Relativity:

    Curvature Radius: ------------RCurvature = 2GoM/c2
    for HyperMass:----------------MHyper = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole

    HyperMass MHyper describes a higher dimensional Inflaton mass for a lower dimensional Instanton curvature radius and becomes the relationship between the beginning and the end of the string epoch in the Planck Radius of the Inflaton and the physicalized wormhole of the Quantum Big Bang as the Instanton.
    The wormhole of the Instanton rwormhole=rps=rmin then forms the displacement quantum for the expanding cosmology in both the classical geometry of General Relativity (GR) and the quantum geometry of Quantum Relativity (QR).

    Using the Schwarzschild metric for a mass of 70 kg would calculate a Curvature Radius for a mass equivalent Black Hole of (2.22..x10-10)(70)/c2 = 1.728..x10-25 meters*.
    This is below the boundary condition of rmin = 10-22/2π m = 1.591549..x10-23 m* for which the minimum mass requirement is found to be 6445.775.. kg*.

    This result shows, that no physical microquantum Black Holes can exist, but that the minimum unitary wormhole quantum of the Instanton is given by a 'wormhole substance' or Inflaton Black Hole Molarity count for a new minimum Planck Oscillator at the HE 8x8 Instanton energy scale EoBigBang=½mpsc2=½hfps=½kTps=½Eps=1/2e*

    MHyper/½mps = 2hc3.e*/4πGo.mps = NAvagadro-Instanton = rps/Rps
    NAvagadro-Instanton = 5.8012x1023 for hypermass
    MHyper = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole
    for Rps = Gomps/c2 = rps/NAvagadro-Instanton = 2.743...x10-47 m* in Inflaton membrane space of 11D and string space of 10D

    MHyper/mmin = Mmin/mmin = {n.hc3e*/4πGo}/mmin = {n.rminc2/2Go}/mmin = {hc3.c2/4πGoEmin}{ne*} = {hc3.c2/4πGohfmin}{ne*} = {2πrmin.hc3.c2/4πGohc}{ne*} = {rmin.c2.E/2GoM}{ne*} = rmin/R.{Ene*} for R = 2GoM/c2
    for a generalized energy-mass proportionality c2=E/M in modular membrane duality with ne* = 1/E and ne*E = 1 (Modular Unification) for n.e*hc = n.λmin.

    mHyper/rmin = {rminc2/2Go}/rmin = c2/2Go = n.mmin.Ee*/R = M/Rcurv for de Broglie wave matter mmin = hfmin/c2 = h/cλmin

    Utility of the Schwarzschild metric allows calculation of Black Hole matter equivalents for any mass M>rminc2/2Go say for a planetary mass MEarth = 6x1024 kg for a rcurv = 0.015 meters and for a solar mass MSun = 2x1030 kg* for a rcurv = 4938.3 meters*.

    The curvature of the Inflaton calculates as RHubble-11D = c/Ho = 2GoMBigBang-Seed/c2 = 1.59..x1026 meters* for the Inflaton Mass of 6.47..x1052 kg*.

    For any mass M<rminc2/2Go say for mass conglomerations smaller than 6445.775 kg* as the characteristic HyperMass for the Instanton, the corresponding curvature radius forms in the Inflaton space preceding the Quantum Big Bang at the time instanton of tmin=tps=1/fps=[fss]mod

    The Standard Gravitational Parameter μ= GM = constant = GoM(XnYn)= GoXn.MYn and for (XY)n=1 can be finestructured in a decreasing gravitational constant G(n)=GoXn with a corresponding increase in the mass parameter M as M(n)=MoYn as say for the proto-nucleonic mass of the Instanton mc(nps) as mc(npresent) = mc.Ynpresent = mneutron < mcYnpresent = 1.711752..x10-27 kg* and 958.99 MeV* upper limited

    For a changing Gravitational constant G(npresent) .mneutron(npresent)2 = Gomc2.Ynpresent and is modulated say in A micro-macro Black Hole perturbation
    Mo2/2M.MMaxHawking = 1.000543 ~ 1


    The Black Holed mass equivalence for astrophysical bodies is well formulated in the application of the basic Schwarzschild metric derived from General Relativity.
    Stephen Hawking developed the inverse proportionality between the mass of a Black Hole M and its Temperature T in the form of the Hawking Modulus:

    HM = mPlanck.EoPlanck/k = √{hc/2πGo}{½mPlanck.c2/k} = hc3/4πGok = {MSmin.TSmax} = {mps.Tps.½NAvagadro-Instanton} =
    [c2/4π2]mod.{MMaxHawking .TSmin } = 9.131793821x1023 kg*K* with (mpsTps = Eps2/kc2 = 1.002117..π)

    The Hawking Modulus so has mensuration units [Mass][Temperature] in [kg][K(elvin)], which reduce to [Mass]{Energy] in [kg][J(oules)] for ignoring the Stefan-Boltzmann entropy constant k.

    And so Mmin.Tmax = hc³/4πGok = [c2/4π2]mod.Mmax.Tmin = ½mPlanck.TPlanck = MMaxHawking. [c2/4π2]mod.Tss and the Hawking Mass is determined as MMaxHawking = λmaxπc²/Go = 2.54469..x1049 kg*.

    HyperMass MHyper (nps) = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole = 6445.775 kg at the Instanton boundary n=nps so increases to MHyper(npresent)Ynpresent =hc3.e*/4πGoXnpresent ~ 11,115.59 kg as the projected Instanton boundary mass for the wormhole radius rwormhole = rps = NAvagadro-Instanton.Rps modulating the Inflaton curvature with the Instanton curvature and utilizing npresent=1.1327... for a decreased perturbed G(npresent) = 6.442x10-11 G-string units for the Standard Gravitational Parameter G(n)miYk(n).mjYn-k = Gomc2 = constant for G(n)=GoXn.


    Using the λminλmax=1 wavelength modulation in the T-duality of λmin=2πRmin=1/λmax=2π/Rmax, we can see, that this modulation closely approximates the geometric mean of the seedling mass in {1/4π}Mo2/2M.MMax=Mo2/8π.M.MHawking=3.2895..x10102/3.2931..x10102 ~ 0.998910744...

    This also circumscribes the actual to critical density ratio in the omega of the general relativistic treatment of the cosmologies.
    Now recall our applied G value in Gm(n)=Go.and apply our just derived Black Hole Mass modulation coupled to that of the quantum micromasses.

    We had: Gomc²={GoXn+k}.{mcYn}.{mcYk}=Gm(n).mnmax.mnmin and where Gm is the actual G value as measured and which has proved difficult to do so in the laboratories.
    Gm(n)=Go.Xn+k=Gomc²/mnmax.mnmin=Gomc²/({mcYn}{mnmin}) and where we have mnmin=mcYk} for the unknown value of k with mnmax=mcYn.

    So Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking.mav} for Xk={mc/mav}.{Mo2/8π.M.MHawking}=1.00109044..{mc/mav}
    and where now {mnmin}={8π.M.MHawking.mav/Mo2}=1.00109044..mav.
    mav={Mo²/8π.M.MHawking}{mnmin}={Mo²/8π.M.MHawking}{mcYk}=0.9989107..{mcYk} and obviously represents a REDUCED minimum mass mnmin=mcYk.

    But the product of maximum and 'new' minimum now allows an actual finetuning to a MEASURED nucleon mass mN by:
    mN² = mavYn.mcYn=mav.mnmax.Yn.

    So substituting for mav in our Gm expression, will now give the formulation:
    Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking.mav}
    Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking}{mcY2n/mN2}
    Gm(n)=Go.{mc2/mN2}{Mo2/8π.M.MHawking}Yn

    The average nucleon mass mN is upper bounded in the neutron mass and lower bounded in the proton mass, their difference being an effect of their nucleonic quark content, differing in the up-down transition and energy level and because of electro charges increasing the intra-quarkian Magneto charge coupling between the two mesonic rings of the neutron and the single mesonic ring in the proton's down- or KIR-quark.

    For a Neutron Restmass of: mneutron=1.6812656x10-27 kg* (941.9111 MeV*) or (1.6749792x10-27 kg and 939.594 MeV)
    the substitution (and using calibrations m=1.001671358 m*; s=1.000978395 s*; kg=1.003753127 kg* and C=1.002711702 C* gives:
    G(np)= Go{mc/mneutron}2.(0.9989107..)Ynp = 6.670693x10-11 (m3/kgs2)* or 6.675312x10-11 (m³/kgs²).

    For a Proton Restmass of: mproton=1.6788956x10-27 kg* (940.5833 MeV*) or (1.672618x10-27 kg and 938.270 MeV).
    G(np) = Go{mc/mN}2.(0.9989107..)Ynp = 6.6895399x10-11 (m3/kgs2)* or 6.694171x10-11 (m³/kgs²).

    Gm(n)=Go.Xn+k = 6.670693x10-11 (m3/kgs2)* then gives kp =ln{Gm(np)/Go}/ln{X} - np = 1.0602852 - 1.132711 = -0.0724258

    The upper value of the neutron bound so represents an upper limit for the Gravitational Constant as the original quark-lepton bifurcation of the X-Boson precursor given in the KKK kernel. Only the KKK kernel is subject to the mass evolution of the cosmos; the leptonic masses being intrinsically incorporated in the Kernel means.
    The mc.Yn so serves as an appropriate upper bounded approximation for G(n), subject to leptonic ring IR-OR perturbations.

    The best approximation for 'Big G' hence depends on an accurate determination for the neutron's inertial mass, only fixed as the base nucleon minimum mass at the birth of the universe. A fluctuating Neutron mass would also result in deviations in 'G' independent upon the sensitivity of the measuring equipment. The inducted mass difference in the protonic-and neutronic restmasses, derives from the Higgs-Restmass-Scale and can be stated in a first approximation as the groundstate.
    Basic nucleon restmass is mc=√Omega.mP=9.9247245x10-28 kg* or 958.99 MeV*.

    (Here Omega is a gauge string factor coupling in the fundamental force interactions as:
    Cuberoot(Alpha):Alpha:Cuberoot(Omega):Omega and for Omega=G-alpha.)
    KKK-Kernelmass=Up/Down-HiggsLevel=3x319.66 MeV*= 958.99 MeV*, using the Kernel-Ring and Family-Coupling Constants.

    Subtracting the Ring-VPE (3L) gives the basic nucleonic K-State as 939.776 MeV*. This excludes the electronic perturbation of the IR-OR oscillation.

    For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
    An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and 2-1/3=5/3 electron energy from the neutron' singular up-quark to relate the trisected nucleonic quark geometric template.

    Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
    Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

    This is the groundstate from the Higgs-Restmass-Induction-Mechanismand reflects the quarkian geometry as being responsible for theinertial mass differential between the two elementary nucleons. All groundstate elementary particle masses are computed from theHiggs-Scale and then become subject to various finestructures. Overall, the MEASURED gravitational constant 'G' can be said to be decreasing over time.

    The ratio given in k is GmYn/Go ~ 0.600362... and so the present G-constant is about 60% of the one at the Planck Scale.
    G decreases nonlinearly, but at a present rate of 0.600362/19.12x109 per year, which calculates as 3.1400..x10-11 G-units per year.

    Generally using the exponential series expansion, one can indicate the change in G.
    For Xn+k=z=exp[(n+k)lnX] by (n+k)lnX=lnz for the value u=(n+k)lnX=-0.481212(n+k); z transforms in exponential expansion eu=1+u+u2/2!+u3/3!+u4/4!+...

    For a function f(n)=z=Gm(n)/Go=Xn+k - f(n)=1-(0.481212.)(n+k)+(0.2316.)(n+k)2/2-(0.1114.)(n+k)3/6+(0.0536.)(n+k)4/24-...+...​

    At timeinstantenuity of the Quantum Big Bang, n=npsps/Rmax=6.2591x10-49 ~ 0
    Then GBigBang=GoXnps=Go (to 50 decimal places distinguishing the timeinstanton from the Nulltime as the Planck-Time transform).
    Go represents the quantum gravitational constant applicable for any Black Hole cosmology and can be used to correlate the MOND gravitation with the Newton-Einstein gravitation (previously stated in section 3.8).

    For our previously calculated k=ln(GmYn/Go)/lnX and which calculates as k= -0.0724258..
    f(n)=1-(0.481212.)(n+k)+(0.2316.)(n+k)2/2-(0.1114.)(n+k)3/6+(0.0536.)(n+k)4/24-(0.0258.)(n+k)5/120+...-...
    for f(1.132711)=1-0.51022+0.13016-0.02214+0.00283-0.000288...+...~ 0.6006340 to fifth order approximation to 0.60036246...

    Hence, the gravitational constant assumes a value of about 60.0% of its Big Bang initialisation and calculates as 6.675x10-11 G-units for a present cycletime npresent=Hotpresent=1.132711...

    The introduction of the mass seed coupling between the macro quantum Mo and the micro quantum mc=mPalpha9 (from the gravitational finestructure unification) PERTURBS the 'purely electromagnetic' cosmology in the perturbation factor k and increases the purely electromagnetic Gmemr in the black hole physics described.

    So gravity appears stronger when one 'looks back in time' or analyses cosmological objects at large distances. The expansion parameter (a) in the Friedmann-Einstein standard cosmology can be rewritten as a curvature ratio R(n)/Rmax={n/(n+1)} and describes the asymptotic universe in say 10 dimensions evolving under the inertial parameters of the c-invariance. This 'lower dimensional universe' is open and expands under hyperbolic curvature under the deceleration parameter qo=½Ωo=Mo/2M=2GoHoMo/c³ ~0.014015... This open universe is bounded in the 'standing wave' of the Hubble Oscillation of the 11D and 'higher dimensional universe'.
     
    Last edited: Sep 25, 2018
  2. admin

    admin Well-Known Member Staff Member

    Messages:
    3,158
    Yn = RHubble/rWeyl = 2πRHubbleWeyl = ωWeyl/Ho = 2πnWeyl = nps/2π = 1.003849x1049

    2nd Inflaton/Quantum Big Bang redefines for k=1: RHubble(1) = n1RHubble = c/Ho(1) = (234.472)RHubble = 3.746x1028 m* in 3.957 Trillion Years for critical nk
    3rd Inflaton/Quantum Big Bang redefines for k=2: RHubble(2) = n1n2RHubble = c/Ho(2) = (234.472)(245.813)RHubble = 9.208x1030 m* in 972.63 Trillion Years for critical nk
    4th Inflaton/Quantum Big Bang redefines for k=3: RHubble(3) = n1n2n3RHubble = c/Ho(3) = (57,636.27)(257.252)RHubble = 2.369x1033 m* in 250.24 Quadrillion Years for critical nk
    5th Inflaton/Quantum Big Bang redefines for k=4: RHubble(4) = n1n2n3n4RHubble = c/Ho(4) = (14,827,044.63)(268.785)RHubble = 6.367x1035 m* in 67.26 Quintillion Years for critical nk
    ...
    (k+1)th Inflaton/Quantum Big Bang redefines for k=k: RHubble(k) = RHubble Π nk = c/Ho Π nk
    .....

    nk = ln{ωWeylRHubble(k)/c}/lnY = ln{ωWeyl/Ho(k)}/lnY

    n1 = 234.471606...
    n2 = 245.812422...
    n3 = 257.251394...
    n4 = 268.784888...



    Dark Energy DE-Quintessence Λk Parameters:

    A general dark energy equation for the kth universe (k=0,1,2,3,...) in terms of the parametrized Milgröm acceleration A(n); comoving recession speed V(n) and scale factored curvature radius R(n):


    Λk (n) = GoMo/Rk(n)2 - 2cHo(Πnk)2/{n-ΣΠnk-1+Πnk)3} for negative Pressure Pk = -Λk(n)c2/4πGoRk

    = {GoMo(n-ΣΠnk-1+Πnk)2/{(Πnk)2.RH2(n-ΣΠnk-1)2} - 2cHo(Πnk)2/{n-ΣΠnk-1+Πnk)3}

    Λo = GoMo(n+1)2/RH2(n)2 - 2cHo/(n+1)3
    Λ1 = GoMo(n-1+n1)2/n12RH2(n-1)2 - 2cHon12/(n-1+n1)3
    Λ2 = GoMo(n-1-n1+n1n2)2/n12n22RH2(n-1-n1)2 - 2cHon12n22/(n-1-n1+n1n2)3
    .....

    Lambda-DE-Quintessence Derivatives:

    Λk'(n) = d{Λk}/dn =
    {GoMo/Πnk2RH2}{2(n-ΣΠnk-1+Πnk).(n-ΣΠnk-1)2 - 2(n-ΣΠnk-1).(n-ΣΠnk-1+Πnk)2}/{(n-ΣΠnk-1)4} - {-6cHo(Πnk)2}/(n-ΣΠnk-1+Πnk)4

    = {-2GoMo/ΠnkRH2}(n-ΣΠnk-1+Πnk)/(n-ΣΠnk-1)3 + {6cHo(Πnk)2}/(n-ΣΠnk-1+Πnk)4

    = {6cHo(1)2}/{(n-0+1)4} - {2GoMo/1.RH2}{(n-0+1)/(n-0)3}........................................ for k=0
    = {6cHo(1.n1)2}/{(n-1+n1)4} - {2GoMo/n1.RH2}{(n-1+n1)/(n-1)3}................................ for k=1
    = {6cHo(1.n1.n2)2}/{(n-1-n1+n1.n2)4} - {2GoMo/n1n2.RH2}{(n-1-n1+n1n2)/(n-1-n1)3}...... for k=2
    .......

    For k=0; {GoMo/3c2RH} = constant = n3/[n+1]5
    for roots nΛmin = 0.23890175.. and nΛmax = 11.97186...
    {GoMo/2c2RH} = constant = [n]2/[n+1]5

    for Λo-DE roots: n+/- = 0.1082331... and n-/+ = 3.40055... for asymptote Λ0∞ = GoMo/RH2 = 7.894940128...x10-12 (m/s2)*

    For k=1; {GoMo/3n13c2RH} = constant = [n-1]3/[n-1+n1]5 = [n-1]3/[n+233.472]5
    for roots nΛmin = 7.66028... and nΛmax = 51,941.9..
    {GoMo/2n14c2RH} = constant = [n-1]2/[n-1+n1]5 = [n-1]2/[n+233.472]5
    for Λ1-DE roots: n+/- = 2.29966... and n-/+ = 7,161.518... for asymptote Λ1∞ = GoMo/n12RH2 = 1.43604108...x10-16 (m/s2)*


    For k=2; {GoMo/3n13n23c2RH} = constant = [n-1-n1]3/[n-1-n1+n1n2]5 = [n-235.472]3/[n+57,400.794]5
    for roots nΛmin = 486.7205 and nΛmax = 2.0230105x108
    {GoMo/2n14n24c2RH} = constant = [n-1-n1]2/[n-1-n1+n1n2]5 = [n-235.472]2/[n+57,400.794]5
    for Λ2-DE roots: n+/- = 255.5865... and n-/+ = 1.15382943...x107 for asymptote Λ2∞ = GoMo/n12n22RH2 = 2.37660590...x10-21 (m/s2)*

    For k=3; {GoMo/3n13n23n33c2RH} = constant = [n-1-n1-n1n2]3/[n-1-n1-n1n2+n1n2n3]5 = [n-57,871.74]3/[n+1.47691729x107]5
    for roots nΛmin = 67,972.496 and nΛmax = 8.3526797...x1011
    {GoMo/2n14n24n34c2RH} = constant = [n-1-n1-n1n2]2/[n-1-n1-n1n2+n1n2n3]5 = [n-57,871.74]2/[n+1.47691729x107]5
    for Λ3-DE roots: n+/- = 58,194.1... and n-/+ = 1.9010262...x1010 for asymptote Λ3∞ = GoMo/n12n22n32RH2 = 3.59120049...x10-26 (m/s2)*



    and where

    Πnk=1=no and Πnk-1=0 for k=0
    with Instanton/Inflaton resetting for initial boundary parameters

    Λo/adeBroglie = {GoMo/Rk(n)2}/ΠnkRHfps2
    = {GoMo(n-ΣΠnk-1+Πnk)2}/{[Πnk]2.RH2(n-ΣΠnk-1)2(ΠnkRHfps2)} = (Πnk)½Ωo

    for Instanton-Inflaton Baryon Seed Constant Ωo = Mo*/MH* = 0.02803 for the kth universal matter evolution

    k=0 for Reset n=nps=Hot and Λo/adeBroglie = GoMo(nps+1)2/{RH3nps2(fps2)} = GoMo/RHc2 = Mo/2MH = ½Ωo
    k=1 for Reset n=1+nps and Λo/adeBroglie = GoMo(1+nps-1+n1)2/{[n1]2.RH3(1+nps-1)2(n1fps2)} = Mo/2n1MH = Mo/2MH* = ½Ωo*
    k=2 for Reset n=n1+1+nps and Λo/adeBroglie = GoMo(n1+1+nps-1-n1+n1n2)2/{[n1n2]2.RH3(n1+1+nps-1-n1)2(n1n2fps2)} = ½Ωo**
    k=3 for Reset n=n1n2+n1+1+nps and Λo/adeBroglie = GoMo(n1n2+n1+1+nps-1-n1-n1n2+n1n2n3)2/{[n1n2n3]2.RH3(n1n2+n1+1+nps-1-n1-n1n2)2(n1n2n3fps2)} = ½Ωo***
    ......

    with nps = 2πΠnk-1.Xnkps/RH = Hotps = Ho/fps = ctps/RH and RH=2GoMH/c2

    No=Hoto/no=Hot=n
    N1=Hot1/n1=(n-1)/n1
    N2=Hot2/n1n2=(n-1-n1)/n1n2
    N3=Hot3/n1n2n3=(n-1-n1-n1n2)/n1n2n3
    ....
    dn/dt=Ho
    .....

    Nk=Hotk/Πnk=(n-ΣΠnk-1)/Πnk
    tk = t - (1/Ho)ΣΠnk-1 for no=1 and No=n

    to=t=n/Ho=No/Ho=nRH/c
    t1=t-1/Ho=(n-1)/Ho=[n1N1]/Ho
    t2=t-(1+n1)/Ho=(n-1-n1)/Ho=(n1n2N2)/Ho
    t3=t-(1+n1+n1n2)/Ho=(n-1-n1-n1n2)/Ho=(n1n2n3N3)/Ho
    .......

    R(n)=R(No)=noRH{n/[n+1]}=RH{n/[n+1]}
    R1(N1)=n1RH{N1/[N1+1]}=n1RH{[n-1]/[n-1+n1]}
    R2(N2)=n1n2RH{N2/[N2+1]}=n1n2RH{[n-1-n1]/[n-1-n1+n1n2]}
    R3(N3)=n1n2n3RH{N3/[N3+1]}=n1n2n3RH{[n-1-n1-n1n2]/[n-1-n1-n1n2+n1n2n3}
    .......


    Rk(n) = ΠnkRH(n-ΣΠnk-1)/{n-ΣΠnk-1+Πnk}

    .....= RH(n/[n+1]) = n1RH(N1/[N1+1]) = n1n2RH(N2/[N2+1]) =.....



    Vk(n) = dRk(n)/dt = c{Πnk}2/{n-ΣΠnk-1+Πnk}2

    .....= c/[n+1]2 = c/[N1+1]2 = c/[N2+1]2 =.....
    .....= c/[n+1]2 = c(n1)2/[n-1+n1]2 = c(n1n2)2/[n-1-n1+n12n22]2 =.....



    Ak(n) = d2Rk(n)/dt2 = -2cHo(Πnk)2/(n-ΣΠnk-1+Πnk)3

    .....= -2cHo/(n+1)3 = -2cHo/n1(N1+1)3 = -2cHo/n1n2(N2+1)3=.....
    ..... = -2cHo/[n+1]3 = -2cHo{n1}2/[n-1+n1]3 = -2cHo(n1n2)2/[n-1-n1+n1n2]3 =.....

    GoMo is the Gravitational Parameter for the Baryon mass seed; Curvature Radius RH = c/Ho in the nodal Hubble parameter Ho and c is the speed of light


    Hubble Parameters:

    H(n)|dS = {Vk(n)}/{Rk(n)} = {c[Πnk]2/[n-ΣΠnk-1+Πnk]2}/{Πnk.RH[n-ΣΠnk-1]/(n-ΣPnk-1+Πnk)} = ΠnkHo/{[n-ΣΠnk-1][n-ΣΠnk-1+Πnk]}


    H(n)|dS = ΠnkHo/{[n-ΣΠnk-1][n-ΣΠnk-1+Πnk]}

    .....= Ho/{[n][n+1]}=Ho/T(n) = n1Ho/{[n-1][n-1+n1]} = n1n2Ho/{[n-1-n1][n-1-n1+n1n2]} =..... for dS

    H(n)'|dS = Ho/[n-ΣΠnk-1] for oscillating H'(n) parameter between nodes k and k+1 ||nps+ΣΠnk-1 - ΣΠnk||

    H(n)|AdS = H(n)'|AdS = {Vk(n)}/{Rk(n)} = c/{RH(n-ΣΠnk-1)}

    H(n)|AdS = H(n)' = Ho/(n-ΣΠnk-1)

    .....= Ho/n = Ho/(n-1) = Ho/(n-1-n1) =..... for AdS


    For initializing scale modulation Rk(n)Ads/Rk(n)dS + ½ = ΠnkRH(n-ΣΠnk-1)/{ΠnkRH(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)} + ½Πnk = {n - ΣΠnk-1 + Πnk + ½} reset coordinate

    dH/dt = (dH/dn)(dn/dt) = -Πnk.Ho2{(2n-2ΣΠnk-1+Πnk)(n-ΣΠnk-1+Πnk+½Πnk)}/{n2-2nΣΠnk-1+(ΣΠnk-1)2+Πnk[n-ΣΠnk]}2
    = -2ΠnkHo2{[n - ΣΠnk-1 + Πnk]2 - ¼ΣΠnk2}/{(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)}2

    dH/dt|dS = -2ΠnkHo2{[n - ΣΠnk-1 + Πnk]2 - ¼(ΣΠnk)2}/{(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)}2


    .....= -2Ho2([n+1]2-¼)/{n[n+1]}2 = -2n1Ho2{[n-1+n1]2-¼n12}/{[n-1][n-1+n1]}2 = -2n1n2Ho2{[n-1-n1+n1n2]2-¼n12n22}/{[n-1-n1][n-1-n1+n1n2]}2 =.....



    dH/dt = (dH/dn)(dn/dt) = -Hoc/{(RH(n-ΣΠnk-1)2} = -Ho2/{n-ΣΠnk-1}2 for AdS

    dH/dt|AdS = -Ho2/{n-ΣΠnk-1}2

    .....= -Ho2/n2 = Ho2/(n-1)2 = -Ho2/(n-1-n1)2 = .....



    dH/dt + 4πGoρ = - 4πGoP/c2

    dH/dt + 4πGoMo/Rk(n)3 = Λk(n)/Rk(n) = - 4πGoP/c2 = GoMo/Rk(n)3 - 2(Πnk)Ho2/{(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)2} for dS with

    {-4π}P(n)|dS = Moc2/Rk(n)3 - 2Πnk(Hoc)2/{Go(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)2} = Moc2(n-ΣΠnk-1+Πnk)3/{Πnk.RH(n-ΣΠnk-1)}3 - 2ΠnkHo2c2/{Go(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)2}



    Λk(n)/Rk(n) = -4πGoP/c2 = GoMo/Rk(n)3 - dH/dt = GoMo/{RH(n-ΣΠnk-1)}3 - Ho2/{n-ΣΠnk-1}2 for AdS with

    {-4π}P(n)|AdS = Moc2/Rk(n)3 - (Hoc)2/{Go(n-ΣΠnk-1)2} = Moc2/{RH(n-ΣΠnk-1)}3 - Ho2c2/{Go(n-ΣΠnk-1)2}




    Deceleration Parameters:

    qAdS(n) = -Ak(n)Rk(n)/Vk(n)2 = -{(-2cHo[Πnk]2)/(n-ΣΠnk-1+Πnk)3}{ΠnkRH(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}/{[Πnk]2c/(n-ΣΠnk-1+Πnk)}2 = 2(n-ΣΠnk-1)/Πnk

    qAdS+dS(n) = 2(n-ΣΠnk-1)/Πnk

    qdS(n) = 1/qAdS+dS(n) - 1 = Πnk/{2[n-ΣΠnk-1} - 1

    with Ak(n)=0 for AdS in areset = Rk(n)AdS/Rk(n)dS + ½ = {RH(n-ΣΠnk-1)}/{RH(n-ΣΠnk-1)/(n-ΣΠnk-1+1)} + ½ = n-ΣΠnk-1+1+½


    Scalefactor modulation at Nk = {n-ΣΠnk-1}/Πnk = ½ reset coordinate


    .....= 2n = 2(n-1)/n1 = 2(n-1-n1)/(n1n2) = 2(n-1-n1-n1n2)/(n1n2n3) = ..... for AdS

    .....= 1/{2n} -1 = n1/{2[n-1]} -1 = n1n2/{2(n-1-n1)} -1 = n1n2n3/{2(n-1-n1-n1n2)} -1 = ..... for dS

    Dark Energy Initiation for qdS=1 with qAdS=1

    k=0 for n = ½ = 0.50000 for qdS=0 with qAdS=1
    k=1 for n = ½n1+1 = 118.236.. for qdS=0 with qAdS=1
    k=2 for n = ½n1n2+n1+1 = 29,053.605.. qdS=0 with qAdS=1
    k=3 for n = ½n1n2n3+n1n2+n1+1 = 7,471,394.054.. qdS=0 with qAdS=1




    Temperature:

    T(n) ={Moc2/(1100σπ2.Rk(n)2.tk)} and for tk = (n-ΣΠnk-1)/Ho

    Tk(n) ={HoMoc2(n-ΣΠnk-1+Πnk)2/[1100σπ2.RH2.(n-ΣΠnk-1)3]}
    ={(Ho3Mo(n-ΣΠnk-1+Πnk)2)/[1100σπ2(n-ΣΠnk-1)3]} = {18.199(n-ΣΠnk-1+Πnk)2/(n-ΣΠnk-1)3}

    T(n) .....= {18.2[n+1]2/n3} ={18.2[n-1+n1]2/(n-1)3} = {18.2[n-1-n1+n1n2]2/(n-1-n1)3} =.....



    Comoving Redshift:

    z + 1 = √{(1+v/c)/(1-v/c)} = √{([n-ΣΠnk-1+Πnk]2+[Πnk]2)/([n-ΣΠnk-1+Πnk]2-[Πnk]2)} =
    √{([n-ΣΠnk-1]2+2Πnk(n-ΣΠnk-1)+2(Πnk)2)/([n-ΣΠnk-1]2+2Πnk(n-ΣΠnk-1)} = √{1 + 2(Πnk)2/{(n-ΣΠnk-1)(n-ΣΠnk-1+2Πnk)}

    z+1 = √{ 1 + 2/{[n2-2nΣΠnk-1 +(ΣΠnk-1)2+2n-2ΣΠnk-1} = √{1+2/{n(n+2-2ΣΠnk-1) + ΣΠnk-1(ΣΠnk-1-2)}}

    ....= √{1+2/(n[n+2])} = √{1+2/([n-1][n-1+2n1])} = √{1+2/([n-1-n1][n-1-n1+2n1n2])} =......




    Baryon-Dark Matter Saturation:

    ΩDM = 1-ΩBM until Saturation for BM-DM and Dark Energy Separation

    ρBM+DM/ρcritical = ΩoY{[n-ΣΠnk-1]/Πnk}/{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = MoY{[n-ΣΠnk-1]/Πnk}/{ρcriticalRk(n)3}

    Baryon Matter Fraction ΩBM = ΩoY{Nk} = Ωo.Y{[n-ΣΠnk-1]/Πnk}

    Dark Matter Fraction ΩDM = ΩoY{[n-ΣΠnk-1]/Πnk}{1-{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3/{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = ΩoY{[n-ΣΠnk-1]/Πnk}{(n-ΣΠnk-1+Πnk)3-(n-ΣΠnk-1)3}/{n-ΣΠnk-1}3
    = ΩoY{[n-ΣΠnk-1]/Πnk}{(1+Πnk/[n-ΣΠnk-1])3 -1} = ΩBM{(1+Πnk/[n-ΣΠnk-1])3 -1}

    Dark Energy Fraction ΩDE = 1- ΩDM - ΩBM = 1 - ΩBM{(1+Πnk/[n-ΣΠnk-1])3}

    ΩBM=constant=0.0553575 from Saturation to Intersection with Dark Energy Fraction

    ΩoY{[n-ΣΠnk-1]/Πnk} = ρBM+DMRk(n)3/MH = [Nk]3/[Nk+1]3 = {(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = Rk(n)3/VH = VdS/VAdS
    for ρBM+DM = MH/RH3 = ρcritical and for Saturation at Ni = 6.541188... = constant ∀ Ni

    (Mo/MH).Y{[n-ΣΠnk-1]/Πnk} = {(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 with a Solution for f(n) in Newton-Raphson Root Iteration and first Approximation x0

    xk+1 = xk - f(n)/f'(n) = xk - {(Mo/MH).Y{[n-∑∏nk-1]/Πnk} - (n-∑∏nk-1)/(n-ΣΠnk-1+Πnk)3}/{(Mo/MH).[lnY]Y{[n-ΣΠnk-1]/Πnk} - 3(n-ΣΠnk-1)2/(n-ΣΠnk-1+Πnk)4}

    x1 = x0 - {(Mo/MH).Y[n] - (n/n+1)3}/{(Mo/MH).[lnY]Y[n] - 3n2/[n+1]4}
    = x0 - {(Mo/MH).Y{N0} - (N0)3/(N0+1)3}/{(Mo/MH).[lnY]Y{N0} - 3(N0)2/1(N0+1)4}
    x1 = x0 - {(Mo/MH).Y{[n-1]/n1} - (n-1)3/(n-1+n1)3}/{(Mo/MH).[lnY]Y{[n-1]/n1} - 3(n-1)2/(n-1+n1)4}
    = x0 - {(Mo/MH).Y{N1} - (N1)3/(N1+1)3}/{(Mo/MH).[lnY]Y{N1} - 3(N1)2/n1(N1+1)4}
    x1 = x0 - {(Mo/MH).Y{[n-1-n1]/n1n2} - (n-1-n1)3/(n-1-n1+n1n2)3}/{(Mo/MH).[lnY]Y{[n-1-n1]/n1n2} - 3(n-1-n1)2/(n-1-n1+n1n2)4}
    = x0 - {(Mo/MH).Y{N2} - (N2)3/(N2+1)3}/{(Mo/MH).[lnY]Y{N2} - 3(N1)2/n1n2(N2+1)4}
    .......


    n = 1.N0 = Ni = 6.541188....⇒ Ni ∀i for ∏nk = n0 = 1
    n = n1N1+1 = (234.472)(6.541188...)+1 = 1534.725.... for ∏nk = n0n1 = n1
    n = n1n2N2+1+n1 = (234.472x245.813)(6.541172)+1+234.472 = 377,244.12.... for ∏nk = n0n1n2 = n1n2
    n = n1n2n3N3+1+n1+n1n2 = (234.472x245.813x257.252)(6.541172)+1+234.472+(234.472x245.813) = 97,044,120.93.... for ∏nk = n0n1n2n3= n1n2n3
    ......




    Baryon-Dark Matter Intersection:

    Nk=√2 for n = √2.Πnk + ΣΠnk-1
    n0 = 1.√2 + 0 = no
    n1 = n1√2 + 1 = 332.593 = n1√2 + 1
    n2 = n1n2√2 + 1 + n1 = 81,745.461
    n3 = n1n2n3√2 + 1 + n1 +n1n2 = 21,026,479.35

    .....




    Hypermass Evolution:

    Yk{(n-ΣΠnk-1)/Πnk} = 2πΠnk.RHps = Πnk.RH/rps = ΠnkMH*k/mH*k for MH = c2RH/2Go and mH = c2rps/2Go

    Hypermass MHyper = mH.Yk{(n-ΣΠnk-1)/Πnk}

    .....= Yn = Y([n-1]/n1) = Y([n-1-n1]/n1n2) =.....

    k=0 for MHyper = MH = 1.MH = mH.Y{(n)} with n = 1.{ln(2π/nps)/lnY} = n1
    = 234.472

    k=1 for MHyper = n1.MH = MH* = mH.Y{(n-1)/n1} with n = [1] + n1.{ln(2πn1/nps)/lnY} = [1] + n1n2
    = 1 + 234.472x245.812 = 57,637.03

    k=2 for MHyper = n1n2.MH = MH** = mH.Y{(n-1-n1)/n1n2} with n = [1 + n1] + n1n2.{ln(2πn1n2/nps)/lnY} = [1 + n1] + n1n2n3
    = 235.472 + 234.472x245.812x257.251 = 14,827,185.4

    k=3 for MHyper = n1n2n3.MH = MH*** = mH.Y{(n-1-n1-n1n2)/n1n2n3} with n = with n = [1 + n1 + n1n2] + n1n2n3.{ln(2πn1n2n3/nps)/lnY} = [1 + n1 + n1n2] + n1n2n3n4
    = 57,871.74 + 234.472x245.812x257.251x268.785 = 3,985,817,947.8
     
    Last edited: Feb 28, 2018
  3. admin

    admin Well-Known Member Staff Member

    Messages:
    3,158
    Cosmology Evolution of the Multiverse

    n
    for k=0; 1; 2; 3; ...universes
    Scalefactor
    a=ao=n/[n+1]



    Redshift
    z0=f(zm)

    comoving
    z=zo=
    √(1+2/
    n[n+2])
    -1


    Time
    t=to=n/Ho
    =nRH/c


    M-G-T-P
    years; s*;
    My;Gy;Ty;Py



    Temp T0
    T=To=
    ∜(18.2
    [n+1]2/n3)


    K* in
    conifolded
    dS

    Ro=aoRHubble

    REvent=nRH

    RParticle=T(n)RH

    Rylem =
    √kTRe3/Gomc2


    m*

    H=Ho/T[n] and H'=Ho/n
    ||nps- 1||

    dH/dt=
    -2H2([n+1]2-¼) dS

    -Ho2/n2 AdS

    (s-1/s-2)*
    (km/Mpcs)*


    Dec-Par

    qdS=
    1/2n -1


    qAdS=2n

    Vo=vrecession

    Ao=amilgröm

    (ms-1/ms-2)*

    BM-DM

    ΩBM=MoYn/MH
    to BM∩DM

    ΩDMBMx
    [1+1/n]3-1}

    after saturation

    DE %
    Pressure
    Lambda DE


    Λ0=GoMo/R02
    -2cHo/[n+1]3

    Λ0/R0=GoMo/R03
    -2Ho2/[n][n+1]2

    -P00c2/4πGoR0

    s-2*; (Jm-3)*

    HyperMass

    MHyper=
    c2rpsYn/2Go


    kg*
    nGenesis=Honps
    Hoλps/RH = Ho2/fps
    1.175x10-66
    - - -
    7.545x1037
    T=
    hRH/kλps
    - - - -E=hF=kT=Mc2-
    M=hRHpsc2
    =0.0118346323
    (33/20)12mcNAv
    nStoney=HotS
    7.019x10-62
    Planck Oscillation
    - -tS=2πλS/c
    =2π[e/c3
    3.738x10-44
    s*

    TS=
    mSc2/k
    7.937x1033
    lS=lP√alpha
    =[e/c2]
    1.7850x10-36
    -----mS=h/lSc
    1.2450x10-6
    nPlanckI=HotP
    Ho√(hGo/2πc5)
    8.217x10-61
    - -tP=2πlP/c =
    √(2πhGo/c5)
    4.376x10-43
    s*


    TP=
    mPc2/k

    1.079x1032
    lP=√(hGo/2πc3)
    2.090x10-35
    - - - - -
    mP=√(hc/2πGo)
    =1.692569x10-8
    nMonopoleIIB=Hotm
    2.886x10-58
    Selfdual Bn coupling
    - -tm=h/mmc2 =
    1.5370x10-40
    s*

    Tm=
    mmc2/k
    3.072x1029
    4.6110x10-32
    de Broglie λ=h/mmc
    - - - - -mm=[ec]
    4.819369x10-11
    nXLBosonHO32=HotXL
    4.134x10-57
    HO32|coupling|HE64
    - -tXL=h/mXLc2 =
    2.2016x10-39 s*

    TXL=
    mXLc2/k
    2.145x1028
    6.6048x10-31
    de Broglie
    λ=h/mXLc
    - - - - -
    mXL=
    alpha.mps/ec]

    3.36455x10-12
    nCosmicRayIIA=HotCR
    1.243x10-51
    IIB|coupling|IIA
    - -tCR=h/mCRc2 =
    6.6182x10-34
    s*

    TCR=
    mCRc2/k
    7.135x1022
    1.9855x10-25
    de Broglie
    λ=h/mCRc
    - - - - -mCR=hA/2ec2
    =1/{B(0)c2}
    1.1192x10-17
    nFalseVacuum
    HotdBmin=2.435x10-50
    De Broglie Matter
    Wave Inflaton
    Quantum
    Oscillation
    2.435x10-50 -

    tdBmin=
    1.297x10-32
    s*

    1/F=nps

    7.545x1037
    T=
    hRH/kλps
    RH=1.5977x1026 - -vdB=RHfps
    4.7930x1056
    adB=RHfps2
    1.4379x1087
    E=hF=kT=Mc2 -
    M=hRH/λpsc2
    =0.0118346323
    (33/20)12mcNAv
    nFalseVacuum
    HotdBmax=5.347x10-50
    De Broglie Matter
    Wave Inflaton
    Quantum
    Oscillation
    5.347x10-50-tdBmax=[√α]tps
    2.847x10-32
    s*

    1/F=nps
    7.545x1037
    T=
    hRH/kλps
    RH=1.5977x1026--vdB=RHfps
    4.7930x1056
    adB=RHfps2
    1.4379x1087
    E=hF=kT=Mc2-M=hRH/λpsc2
    =0.0118346323
    (33/20)12mcNAv


    k=0 initiated
    n=nps
    1st Instanton
    from 1st Inflaton
    RE=noRH=RH


    npsps/RH=Ho/fps
    Instanton HE64
    Quantum Big Bang
    Max DE


    Quantum Tunnel 1
    String Era to k=0
    6.26x10-49 1.26x1024

    tps=
    3.333x10-31
    s*

    Tps=
    2.935x1036
    λps=2πrps=10-22
    1.0001x10-22
    1.0001x10-22
    H|dS=Ho/Tn=c/λps=fps
    H'=Ho/n=
    c/nRH=3x1030


    dH/dt|dS=
    -2Ho2([n+1]2-¼)/
    ([n][n+1])2
    =-(1.5/nps2) Ho2
    =-3.8289x1096 Ho2


    dH/dt|AdS=
    -Ho2/n2
    =-Ho2/{nps2}=-fps2
    =-9x1060

    qdS=
    1/2n -1
    =1/2nps- 1

    qAdS=2n
    =2nps


    7.988x1047
    1.252x10-48
    c=3x108
    -2cHo=-2Ho2/RH
    -1.12664x10-9
    0.02803
    0.97197
    1





    0
    Λo=
    GoMops2-2cHo
    =2.01522x1085

    Λo/Ro=
    GoMops3
    -2Ho2RHps
    =GoMops3
    -2Hofps
    =2.01522x10107


    -P=Λoc2/4πGoRo
    =1.2990x10133

    n≥nps

    mH=6445.7752
    mps=2.222x10-20

    Yn=2πRHps
    =MH/mH
    n=3.562x10-27
    Bosonic Unification
    3.562x10-271.68x10131.897x10-9
    s*
    hfps/k=
    1.417x1020
    0.569092H=Ho/Tn=5.27x108
    H'=c/nRH=5.27x108
    -1.1822x1053 Ho2
    -7.8813x1052 Ho2
    1.4037x1026
    7.124x10-27
    c
    -1.12664x10-9
    0.02803
    0.97197
    1

    0
    6.2224x1041
    1.0934x1042
    7.0478x1067
    6,445.775

    n=5.145x10-21
    Electro-Weakon
    Separation
    298.785 GeV*
    Higgs/XL Expectation
    5.145x10-211.39x10100.00274
    s*
    3.400x1015822,004.02H=Ho/Tn=364.96
    H'=c/nRH=364.96
    -5.6666x1040 Ho2
    -3.7778x1040 Ho2
    9.718x1019
    1.029x10-20
    c
    -1.12664x10-9
    0.02803
    0.97197
    1

    0
    2.9825x1029
    3.6283x1023
    2.3387x1049
    6,445.775
    nG=2.1228x10-15
    Ylem-G Protostar
    RGps∛{G}/2π
    =3.391558x1011 m*
    2.1228x10-152.170x107
    1130.515
    s*
    Meson VPE Inner

    Primordial
    Neutron Decay

    2.089x10113.39156x1011
    -
    -
    Rylem=24,029.3
    H=Ho/Tn=8.85x10-4
    H'=c/nRH=8.85x10-4
    -3.3287x1029 Ho2
    -2.2191x1029 Ho2

    2.3554x1014
    4.2456x10-15
    c
    -1.12664x10-9
    0.02803
    0.97197
    1

    0
    1.7520x1018
    5.1657x106
    3.3297x1032
    6,445.775
    nF=2.1601x10-15
    Ylem=F-Protostar
    RFps∛{F}/2π
    =3.4510775x1011m*
    2.1601x10-152.152x107
    1150.380
    s*
    Meson VPE

    Outer
    Primordial
    Neutron Decay
    2.061x10113.45108x1011
    -
    -
    Rylem=23,872.9
    H=Ho/Tn=8.69x10-4
    H'=c/nRH=8.69x10-4
    -3.2147x1029 Ho2
    -2.1431x1029 Ho2

    2.3147x1014
    4.3202x10-15
    c
    -1.12664x10-9
    0.02803
    0.97197
    1

    0
    1.6921x1018
    4.9027x106
    3.1602x1032
    6,445.775
    nE=2.1506x10-12
    Ylem-E-Planetesimal
    REps∛{E}/2π
    =3.4359711x1014 m*
    2.1506x10-12681,8351,145,320.3
    13d6h8m
    40.3s*
    1.163x1093.43597x1014
    -
    -
    Rylem=1,793.13
    H=Ho/Tn=8.73x10-7
    H'=c/nRH=8.73x10-7
    -3.2432x1023 Ho2
    -2.1621x1023 Ho2

    2.3249x1011
    4.3012x10-12
    c
    -1.12664x10-9
    0.02803
    0.97197
    1

    0
    1.7070x1018
    4.9680x10-3
    3.2023x1023
    6,445.775
                
    n=2.3x10-5
    Recombination
    Start
    2.30x10-5293.9388,141.5 y29453.6746x1021
    -
    -
    H=Ho/Tn=8.16x10-14
    H'=c/nRH=8.16x10-14
    -2.8356x109 Ho2
    -1.8904x109 Ho2

    21,738.13
    4.6x10-5
    0.999954 c
    -1.12656x10-9
    0.02803
    0.97197
    1

    0
    0.01492
    4.0617x10-24
    261.8076
    6,445.8
    n=6.3x10-5
    Recombination
    End
    6.30x10-5177.21.0632 My2935λss=1/λps=1022
    -
    -

    H=Ho/Tn=2.98x10-14
    H'=c/nRH=2.98x10-14
    -3.7794x108 Ho2
    -2.5195x108Ho2

    7935.51
    1.26x10-4
    0.999874 c
    -1.12642x10-9
    0.02803
    0.97197
    1

    0
    2.0152x10-3
    1.9766x10-25
    12.7409
    6,446.0
    n=0.0003934253.93x10-449.4216.6395 My739.532πx1022
    -
    -
    H=Ho/Tn=4.77x10-15
    H'=Ho/n=4.77x10-15
    -9.6935x106 Ho2
    -6.4606x106 Ho2

    1269.89 7.8685x10-4
    0.999214 c
    -1.1253x10-9
    0.02804
    0.971976
    1

    0
    5.1045x10-5
    8.1241x10-28
    0.05237
    6,447.0
    n=0.014015 for adBBM=Mo/2MH
    RSarkar =GoMo/c2
    0.013827.478236.5186 My51.0622.2391x1024
    -
    -
    H=70.37 Ho=4084.04
    H'=Ho/n=4141.28
    -7706.57 Ho2
    -5091.13 Ho2

    34.6761
    0.02803
    0.97255 c
    -1.0806x10-9
    0.02822
    0.97178
    1

    0
    3.9115x10-8
    1.8227x10-32
    1.1749x10-6
    6,489.4
    n=0.02803 for ΩBMo
    Supercluster Seeds
    0.027275.015473.0373 My30.5714.3562x1024
    -
    -
    H=34.703 Ho=2014.2
    H'=Ho/n=2070.64
    -1943.40 Ho2
    -1272.78 Ho2

    16.8380
    0.05606
    0.94621 c
    -1.0370x10-9
    0.02841
    0.97159
    1

    0
    9.5827x10-9
    2.1998x10-33
    1.4179x10-7
    6,533.3
    n=0.056391
    Radiation-DM Equilibrium
    0.053383.2720.9517 Gy18.3358.5285x1024
    -
    -
    H=16.787 Ho=974.30
    H'=Ho/n=1029.24
    -488.04 Ho2
    -314.47 Ho2

    7.8667
    0.112782
    0.89609 c
    -9.5567x10-10
    0.02880
    0.97120
    1

    0
    1.8150x10-9
    2.1281x10-34
    1.3717x10-8
    6,623.1

    n=0.1082331
    Λ0=0 from +/-
    1st Λ0 Root
    0.097662.1251.8265 Gy11.5231.5603x1025
    -
    -
    H=8.337 Ho=483.89
    H'=Ho/n=536.27
    -135.98 Ho2
    -85.365 Ho2

    3.6198
    0.21646
    0.8142 c
    -8.2774x10-10
    0.02953
    0.97047
    1



    0
    0
    1st Λ0 Root +/-
    0
    0
    6,790.4
    n=0.132711
    Critical Redshift
    Boundary Mirror
    for apparent cosmic
    acceleration DE
    0.117161.8402.2396 Gy9.99761.8712x1025
    -
    -
    H=6.652 Ho=386.10
    H'=Ho/n=437.34
    -91.43 Ho2
    -56.779 Ho2
    2.7676
    0.26542
    0.7794 c
    -7.7522x10-10
    0.02988
    0.97012
    1

    0
    -1.9967x10-18

    -1.0689x10-35
    -6.8899x10-10
    6,870.8
    n=0.23890175
    Λ0 = Minimum DE
    Peak of Galaxies Λ0
    0.192831.1774.0317 Gy6.72783.0803x1025
    -
    -
    H=3.379 Ho=196.10
    H'=Ho/n=242.95
    -29.3350 Ho2
    -17.521 Ho2

    1.0929
    0.4748
    0.6515 c
    -5.9248x10-10
    0.03144
    0.96856
    1



    0
    -3.8009x10-10
    Λo Minimum
    -1.2340x10-35
    -7.9538x10-10
    7,231.1

    n=½
    k=0 DE Initiation
    0.333330.6128.4381 Gy4.25445.3256x1025
    -
    -
    H=1.333 Ho=77.39
    H'=Ho/n=116.08
    -7.1111 Ho2
    -4.0000 Ho2

    0
    1
    k=0 DE
    Initiation
    0.4444 c
    -3.3382x10-10
    0.0357
    0.9282
    0.9639

    0.0361
    -2.6276x10-10
    -4.9340x10-36
    -3.1803x10-10
    8,199.2
    n=0.5858
    BM∩DM Image
    0.369400.5239.8860 Gy3.88455.9019x1025
    -
    -
    H=1.076 Ho=62.48
    H'=Ho/n=99.08
    -5.2488 Ho2
    -2.9141 Ho2
    -0.1465
    1.1716
    0.3977 c
    -2.8251x10-10
    0.0372
    0.7008
    0.7380


    0.2620
    -2.2466x10-10
    -3.8065x10-36
    -2.4536x10-10
    8544.8
    n=X=0.6180340.381970.49510.4300 Gy3.76926.1026x1025
    -
    -
    H=Ho=58.04
    H'=Ho/n=93.91
    -4.7361 Ho2
    -2.6180 Ho2
    -0.1910
    1.2361
    0.3820 c
    -2.6596x10-10
    0.0377
    0.6388
    0.6765

    0.3235
    -2.1185x10-10
    -3.4715x10-36
    -2.2376x10-10
    8.678.3
    n=0.86729 = npresent
    dS
    apparent cosmic
    acceleration DE
    0.46446 0.343214.6365 Gy3.14057.4206x1025
    -
    -
    H=0.617 Ho=35.84
    H'=Ho/n=66.92
    -2.4683 Ho2
    -1.3294 Ho2
    -0.4235
    1.7346
    0.28680 c
    -1.7304x10-10
    0.04255
    0.38211
    0.42466

    0.5754
    -1.3644x10-10
    -1.8387x10-36
    -1.1852x10-10
    9,784.3

    1st Mirror Node

    n=1
    Semi Hubble Cycle


    2nd Inflaton
    imaged in {nps}
    0.50000 0.2910to=t-tps=1/Ho
    16.8761 Gy
    2.92108.4837x1025
    1.5977x1026
    3.1954x1026
    H=½ Ho=29.02
    H'=Ho/n=58.04
    -1.8750 Ho2
    -1.0000 Ho2

    2
    0.25000 c
    -1.4083x10-10
    0.04535
    0.31745
    0.36280


    0.6372
    -1.1283x10-10

    -1.3676x10-36
    -8.8153x10-11

    10,429.5


    k=1 initiated
    n=nps+1
    n1=234.472
    2nd Instanton
    from 2nd Inflaton
    RE1=n1RH



    Scalefactor
    {xn1}

    a1=[n-1]
    /[n-1+n1]

    a1<0 for
    n<[1]+n1/
    [n1-1]=
    469.944/
    233.472
    =2.01285


    lim
    {1+1+=2+}


    Redshift z1
    n=1+nps

    [z+1]2 =
    1+2n12/
    {n2+2n[n1-1]
    +1-2n1}
    =1+n1/nps


    1.9356x1025

    Time t1

    t1=t-to
    =(n-1)/Ho
    =(n+nps-1)RH/c






    Temp T14
    18.2
    ([n-1+n1)2
    /{n12
    (n-1)3
    }

    =
    2.936x1036

    R1=n1[n-1]RH/[n-1+n1]
    ps=10-22

    R1E=[n-1]RH
    ps
    =1.0000x10-22


    R1P=
    [n-1+n1]R1E
    =n1λps
    =2.34472x10-20



    H|dS=n1Ho/
    {[n-1][n-1+n1]}
    =fps


    H'=Ho/(n-1)
    =fps=3x1030
    ||nps+1 - n1+1||

    dH/dt|dS=
    -2n1Ho2([n-1+n1]2
    -¼n12)/([n-1][n-1+n1])2


    =-(3n1/2nps2) Ho2
    =-8.9776x1098 Ho2

    dH/dt|AdS=
    -Ho2/(n-1)2

    =-fps2=-9x1060

    qdS=
    n1/2[n-1] -1
    =n1/2nps -1


    qAdS=
    2[n-1]/n1
    =2nps/n1






    1.873x1050
    5.339x10-51

    V1=cn12/
    (n-1+n1)2
    A1=-2cHon12/
    (n-1+n1)3
    =2cHo/n1
    =-4.8050x10-12



    BM-DM
    ΩBM=
    MoYN1/MH


    N1=[n-1]/n1
    to BM∩DM
    ΩDMBM.{[1+1/N1]3-1}
    ={1+n1/[n-1]}3-1

    after saturation

    0.02803
    0.97197
    1






    DE %
    Pressure

    0


    Λ1=GoMo/R12
    -2cHon12/
    [n-1+n1]3
    =GoMops2
    -2cHo/n1
    =2.01522x1085
    Λ1/R1=
    GoMo/R13
    -2Ho2n1/[n-1]
    [n-1+n1]2

    GoMops3
    -2Hofps/n1

    =2.01522x10107

    -P11c2/4πGoR1
    =1.2990x10133

    n≥1+nps

    HyperMass

    MHyper=
    mHY{[n-1]/n1}



    MH*=n1MH
    =1.51717x1055


    mps=2.22x10-20

    Y{[n-1]/n1}
    =2πn1RHps
    =MH*/mH


    mH=6445.775

    n=1.132711↩
    = npresent
    AdS
    imaged in
    {0.132711;0.86729}

    0.53111
    5.6568x10-4
    (0.13264)
    0.25045
    41.039
    19.1158 Gy
    2.23964 Gy
    2.7472
    9.3964
    8.4855x1025
    1.8097x1026
    3.8596x1026
    2.1191x1025
    2.1203x1025
    4.9743x1027
    H=0.414 Ho=24.03
    H'=Ho/[2-n]
    =66.92

    -1.4731 Ho2
    -0.7794 Ho2

    H=7.5309 Ho
    H'=Ho/(n-1)=437.34
    -20,743.89 Ho2
    -56.7788 Ho2

    -0.5586
    2.2654

    882.393
    1.132x10-3

    0.21985 c
    -1.1614x10-10

    0.99886 c
    -4.7969x10-12
    0.04834
    0.27432
    0.32266

    0.02804
    0.97196
    1




    0.677234
    -8.81537x10-11
    -1.0389x10-36
    -6.69636x10-11

    0
    4.4397x10-10
    2.0951x10-35
    1.35047x10-9
    11,117.26
    6,447.6
    n=1.41421=√2↩
    BM∩DM Intersect
    ΩBM=constant
    k=0
    imaged in
    {0.41421;0.58579}
    0.58579
    1.7635x10-3
    (0.41348)
    0.1892
    22.803
    23.8664 Gy
    6.99025 Gy
    2.4747
    4.004
    9.3592x1025
    2.2594x1026
    5.4548x1026
    6.6061x1025
    6.6177x1025 1.5544x1028
    H=0.293 Ho=17.00
    H'=Ho/[2-n]=99.08
    -0.9571 Ho2
    -0.5000 Ho2
    H=2.4104 Ho
    H'=140.12
    -20,129.25 Ho2
    -5.8285 Ho2

    -0.6464
    2.8284

    282.035
    3.533x10-3

    0.1716 c
    -8.0068x10-11

    0.99648 c
    -4.7796x10-12



    0.05536
    0.22005
    0.27541
    BM-DM
    Saturation
    BM∩DM
    Intersect
    ΩBM=constant
    k=0

    0.02805
    0.97195
    1



    0.72459
    -5.7062x10-11
    -6.0969x10-37
    -3.9300x10-11
    0
    4.1400x10-11
    6.2641x10-37
    4.0377x10-11
    12,730.0
    6,451.3
    n=Y=1.618034↩
    imaged in
    {X;1-X}
    0.61803
    2.6289x10-3
    (0.61641)
    0.1583
    18.491
    27.3061 Gy
    10.4300 Gy
    2.3295
    2.9671

    9.8736x1025
    2.5851x1026
    6.7679x1026
    9.8482x1025
    9.8741x1025
    2.32130x1028
    H=0.236 Ho=13.70
    H'=Ho/[2-n]=151.95
    -0.7361 Ho2
    -0.3820 Ho2
    H=1.6138 Ho
    H'=93.91
    -922.40 Ho2
    -2.6180 Ho2

    -0.6910
    3.2361

    188.692
    5.272x10-3

    0.1459 c
    -6.2785x10-11

    0.99475 c
    -4.7672x10-12
    0.05536
    0.17915
    0.23451

    0.02807
    0.97193
    1



    0.76549
    -4.2114x10-11
    -4.2653x10-37
    -2.7493x10-11
    0
    1.6011x10-11
    1.6258x10-37
    1.0480x10-11
    14,041.8
    6,454.0
    n=2
    Full Hubble Cycle
    imaged in
    {nps;1}
    0.66666
    4.2468x10-3
    (0.99575)
    0.1180
    14.329
    33.7522 Gy
    16.8761 Gy
    2.1272
    2.0699

    1.0650x1026
    3.1954x1026
    9.5861x1026
    1.5909x1026
    1.5977x1026
    3.7621x1028

    R1E=RH
    H=0.167 Ho=9.69
    H'=Ho/[n-2]=fps
    -0.4861 Ho2
    -0.2500 Ho2
    H=0.9958 Ho
    H'=58.04
    -352.70 Ho2
    -1.0000 Ho2

    -0.7500
    4.0000

    116.236
    8.530x10-3

    0.1111 c
    -4.1727x10-11

    0.99152 c
    -4.7440x10-12
    0.05536
    0.13148
    0.18684

    0.02809
    0.97191
    1



    0.81316
    -2.3960x10-11
    -2.2499x10-37
    -1.4502x10-11
    0
    3.2183x10-12
    2.0229x10-38
    1.3039x10-12
    16,875.3
    6,459.1




    n=2.29966↪
    imaged in
    {0.29966;0.70034}
    Λ1=0 from +/-
    1st Λ1 Root

    0.69694
    5.5124x10-3
    (1.29250)

    0.0965
    12.450

    38.8093 Gy
    21.9332 Gy

    2.0091
    1.7016

    1.1135x1026
    3.6741x1026
    1.2123x1027
    2.0650x1026
    2.0764x1026
    4.8956x1028




    H=0.132 Ho=7.65
    H'=Ho/[n-2]=193.67
    -0.3695Ho2
    -0.1891Ho2
    H=0.7652 Ho
    H'=44.66
    -208.98 Ho2
    -0.5920 Ho2


    -0.7826
    4.5993

    89.2051
    0.01109


    0.0918 c
    -3.1360x10-11

    0.98901 c
    -4.7260x10-12


    0.05536
    0.10818
    0.16354

    0.02810
    0.97190
    1




    0.83646
    -1.5107x10-11
    -1.3566x10-37
    -8.7447x10-12
    0
    0
    1st Λ1 Root +/-
    0
    0

    19,492.9
    6,463.0
    n=2.4148↪
    imaged in
    {0.4148;0.5858}
    0.70716
    5.9978x10-3
    (1.40631)
    0.0898
    11.893
    40.7524 Gy
    23.8763 Gy
    1.9703
    1.5970
    1.1299x1026
    3.8581x1026
    1.3175x1027
    2.2468x1026
    2.2604x1026
    5.332x1028
    H=0.121 Ho=7.04
    H'=Ho/[n-2]=139.92
    -0.3356 Ho2
    -0.1715 Ho2
    H=0.7025 Ho
    H'=41.02
    -176.43 Ho2
    -0.5000 Ho2

    -0.7929
    4.8296

    81.8640
    0.01207

    0.0858 c
    -2.8294x10-11

    0.98804 c
    -4.7191x10-12
    0.05536
    0.10119
    0.15655

    0.02811
    0.97189
    1



    0.84345
    -1.2509x10-11
    -1.1069x10-37
    -7.1349x10-12
    0
    -7.8752x10-13
    -3.2356x10-39
    -2.0856x10-13
    20,603.4
    6,464.5



    n=3.40055↩
    imaged in
    {0.40055;0.59945}
    Λ0=0 from -/+
    2nd Λ0 Root
    0.77276
    0.010134
    (2.37622)
    0.0530
    8.9084
    57.3880 Gy
    40.5119 Gy
    1.7303
    1.0765
    1.2346x1026
    5.4330x1026
    2.3908x1027
    3.7964x1026
    3.8353x1026
    9.0847x1028
    H=0.067 Ho=3.88
    H'=Ho/[4-n]=96.86
    -0.1707 Ho2
    -0.0865 Ho2
    H=0.4127 Ho
    H'=24.18
    -61.44 Ho2
    -0.1735 Ho2

    -0.8530
    6.8011

    47.8371
    0.02049

    0.0516 c
    -1.3221x10-11

    0.97983 c
    -4.6604x10-12
    0.05536
    0.06461
    0.11997

    0.02817
    0.97183
    1




    0.88003
    0
    2nd Λ0 Root -/+
    0
    0
    0
    -3.2621x10-12
    -8.5926x10-39
    -5.5386x10-13
    33,109.2
    6,477.6


    n=6.541188↪
    DM Saturation BM
    k=0

    0.86739
    0.023087
    (5.41326)

    0.0177
    5.5437

    110.3898 Gy
    93.5137 Gy

    1.3867
    0.5786


    1.3858x1026
    1.0451x1027
    7.8811x1027
    8.6486x1026
    8.8530x1026
    2.1248x1029


    H=0.020 Ho=1.176
    H'=Ho/[n-6]
    =107.25

    -0.0465 Ho2
    -0.0234 Ho2
    H=0.1763 Ho
    H'=10.474
    -11.629 Ho2
    -0.0326 Ho2


    -0.9236
    13.0823

    20.1546
    0.04727


    0.0176 c
    -2.6270x10-12

    0.9544 c
    -4.4798x10-12
    0.05536
    0.02947
    0.08483

    0.02835
    0.97165
    1

    0.91517
    7.8666x10-12
    5.6766x10-38
    3.6590x10-12
    0
    -4.2104x10-12
    -4.8683x10-39
    -3.1380x10-13

    150,073.0
    6,519.5
    n=7.42808↩
    XnBMo
    projected MoYn=MH
    imaged in
    {0.42808; 0.57192}
    0.88135
    0.026684
    (6.25656)
    0.0142
    5.0814
    125.3571 Gy
    108.4810 Gy
    1.3327
    0.5186
    1.4081x1026
    1.1868x1027
    1.0002x1028
    9.9959x1026
    1.0270x1027
    2.4740x1029
    H=0.016 Ho=0.927
    H'=Ho/[8-n]=101.48
    -0.03612 Ho2
    -0.018124 Ho2
    H=0.1514 Ho
    H'=9.029
    -8.54 Ho2
    -0.0242 Ho2

    -0.9327
    14.8562

    17.2381
    0.05483

    0.0141 c
    -1.8819x10-12

    0.94734 c
    -4.4305x10-12
    0.05536
    0.02550
    0.08086

    0.02840
    0.97160
    1



    0.91914
    8.2820x10-12
    5.8816x10-38
    3.7911x10-12
    0
    -4.2288x10-12
    -4.2305x10-39
    -2.7268x10-13
    229,959.9
    6,531.4

    n=7.66028↩
    imaged in
    {0.66028; 0.33972}
    Λ1= Minimum DE
    Peak of Galaxies Λ1

    0.88453
    0.027621
    (6.47632)

    0.0134
    4.9759

    129.2757 Gy
    112.4000 Gy

    1.3201
    0.5052

    1.4132x1026
    1.2239x1027
    1.0728x1028
    1.0347x1027
    1.0641x1027
    2.5659x1029


    H=0.015 Ho=0.875
    H'=Ho/[8-n]=170.85
    -0.02004 Ho2
    -0.01704 Ho2
    H=0.1460 Ho
    H'=8.7143
    -8.07 Ho2
    -0.0225 Ho2




    -0.9348
    15.3206

    16.6023
    0.05681


    0.01704 c
    -1.7346x10-12

    0.9455 c
    -4.4177x10-12

    0.05536
    0.02463
    0.07999

    0.02842
    0.97158
    1

    0.92001
    8.3561x10-12
    5.9129x10-38
    3.8113x10-12
    0
    -4.2295x10-12
    Λ1 Minimum
    -4.0877x10-39
    -2.6348x10-13

    257,145.6
    6534.5



    n=11.97186↩
    imaged in
    {0,9719;0.0281}
    Λ0 = Maximum DE
    Asymptote:
    Λ0 ⇒ GoMo/RH2
    =7.89494x10-12

    0.92291
    0.044702
    (10.4814)

    0.00596
    3.6778

    202.0391 Gy
    185.1630 Gy

    1.1558
    0.3505

    1.4745x1026
    1.9127x1027
    2.4812x1028
    1.6746x1027
    1.7530x1027
    4.3025x1029


    H=0.0064 Ho=0.374
    H'=Ho/[12-n]
    =2065.48

    -0.0139 Ho2
    -6.9771x10-3 Ho2
    0.08706 Ho
    H'=5.289
    -3.01 Ho2
    -8.3068x10-3 Ho2





    -0.9582
    23.9438

    9.6851
    0.0936


    5.9428x10-3 c
    -5.1615x10-13

    0.9126 c
    -4.1890x10-12

    0.05536
    0.01506
    0.07042

    0.02867
    0,97133
    1



    0.92958
    8.7529x10-12
    Λo Maximum
    5.9362x10-38
    3.8263x10-12
    0
    -4.1171x10-12
    -2.4586x10-39
    -1.5847x10-13


    2,047,643.4
    6,592.6

    n=118.236=½n1+1↪
    imaged in
    {0.236;0.764}

    k=1 DE Initiation
    0.99161
    0.333333
    (78.1573)
    7.034x10-5
    0.60909
    1.9954 Ty
    1.9785 Ty
    0.62901
    0.07100
    1.5843x1026
    1.8890x1028
    2.2524x1030
    1.2487x1028
    1.8731x1028
    6.5877x1030

    H=7.2142x10-5 Ho
    H'=Ho/[n-118]
    =245.93

    -1.4306x10-4 Ho2
    -7.1532x10-5 Ho2
    H=5.6865x10-3 Ho
    H'=0.4951
    -0.0303 Ho2
    -7.2758x10-5 Ho2


    -0.9958
    236.472

    0
    1
    k=1 DE
    Initiation

    7.0337x10-5 c
    -6.6460x10-16

    0.44444 c
    -1.4237x10-12
    0.05536
    0.00142
    0.05678


    0.03565
    0.92235
    0.95800

    0.94322
    8.0281x10-12
    5.0673x10-38
    3.2663x10-12
    0.04200
    -1.4224x10-12
    -1.1391x10-40
    -7.3425x10-15
    2.5980x1028
    8,190.7
    n=234.472=n1
    imaged in
    {0.472;0.528}

    Quantum Tunnel n1
    k=0 to k=1
    0.995753
    0.498931
    (116.985)
    1.804x10-5
    0.29247
    3.9569744 Ty
    3.9401098 Ty
    0.528956
    0.04885
    1.5909x1026
    3.7461x1028
    8.8210x1030
    1.8690x1028
    3.7301x1028
    8.7460x1030
    H=1.8112x10-5 Ho
    H'=Ho/[n-234]
    =122.97
    Ho*=Ho/n1
    =8.008325x10-21
    -3.6379x10-5 Ho2
    -1.8189x10-5 Ho2
    H=2.1462x10-3 Ho
    H'=0.2486
    -8.0630x10-3 Ho2
    -1.8346x10-5 Ho2

    -0.9979
    468.944

    -0.4989
    1.99574

    1.804x10-5 c
    -8.6291x10-17

    0.25107 c
    -6.0448x10-13
    0.05536
    0.00071
    0.05607

    0.04526
    0.31915
    0.36441

    0.94393
    7.962x10-12
    5.0050x10-38
    3.2261x10-12
    0.63559
    -6.0391x10-13
    -3.2311x10-41
    -2.0827x10-15

    MH=
    6.4706x1052

    10,408.1
    k=2 initiated
    n=nps+1+n1

    n2=245.813
    3rd Instanton
    from 3rd Inflaton
    RE2=n1n2RH


    Scalefactor
    {xn1n2}

    a2=[n-1-n1]

    /[n-1-n1+n1n2]
    a2<0 for
    n<[1+n1]
    +n1n2/
    (n1n2-1)=
    235.472+
    57,636.037/
    57,635.037


    lim
    {1+n1+1+
    =236.472+}

    Redshift z2
    n=1+n1+nps


    [z+1]2 =
    1+2(n1n2)2
    /{n2+
    2n(n1n2-1-n1)+(1+n1)(1+n1-2n1n2)}
    =1+n1n2/nps

    3.0345x1026

    Time t2

    t2=t-(1+n1)/
    Ho
    =(n-1-n1)/Ho


    tps=
    3.33x10-31


    Temp T24

    18.2
    [(n-1-n1+
    n1n2)2

    /{[n1n2]2
    (n-1-n1)3
    }

    =2.935x1036

    R2=
    n1n2RH(n-1-n1)/
    [n-1-n1+n1n2]

    ps=10-22

    R2E=[n-1-n1]RH
    ps

    R2P=
    [n-1-n1+n1n2]R2E
    =[n1n2ps
    =5.7636x10-18

    H|dS=
    n1n2Ho/
    {[n-1-n1][n-1-n1+n1n2]
    }
    =fps

    H'=Ho/(n-1-n1)=fps

    ||nps+1+n1 - n1n2+ n1+1||

    dH/dt|dS=
    -2n1n2Ho2(
    [n-1-n1+n1n2]2
    -¼n12n22)/([n-1-n1]
    [n-1-n1+n1n2])2

    =-(3n1n2/2nps2) Ho2
    =-2.2068x10101 Ho2

    dH/dt|AdS=
    -Ho2/(n-1-n1)2

    =-fps2=-9x1060
    qdS=n1n2/
    2[n-1-n1]-1
    =n1n2/2nps-1




    qAdS=2[n-1-n1]/n1n2
    =2nps/n1n2



    4.604x1052
    2.172x10-53

    V1=cn12n22/
    (n-1-n1+n1n2)2
    A1=-2cHon12n22/
    (n-1-n1+n1n2)3

    c
    -2cHo/n1n2
    =-1.9547x10-14
    BM-DM
    ΩBM=MoYN2/MH
    N2=[n-1-n1]/n1n2
    to BM∩DM ΩDMBM.{[1+1/N2}3-1}
    ={1+n1n2/[n-1-n1]}3-1
    after saturation

    0.02803
    0.97197
    1





    DE %
    Pressure

    0
    Λ2=
    GoMo/R22
    -2cHon12n22/
    [n-1-n1+n1n2]3
    =GoMops2
    -2cHo/n1n2
    =2.01522x1085
    Λ2/R2=GoMo/R23
    -2Ho2n1n2/
    [n-1-n1]
    [n-1-n1+n1n2]2

    =GoMops3
    -2Hofps/n1n2
    =2.01522x10107


    -P22c2/4πGoR2
    =1.2990x10133

    n≥1+nps+n1
    =235.472


    HyperMass

    MHyper=
    mHY{[n-1-n1]/
    n1n2}


    MH**=n1n2MH
    =3.7294x1057
    mps=2.22x10-20

    Y{[n-1-n1]/n1n2}
    =2πn1n2RHps
    =MH*/mH


    mH=6445.775

    2nd Mirror Node

    n=235.472=1+n1

    =[1]+n1
    =[1+n1]+nps

    3rd Inflaton
    double
    imaged in

    {nps} and {1}
    0.995771
    0.500000
    (117.236)
    1.0860x10-53
    (nps)
    1.7883x10-5
    0.29099
    3.0345x1026


    3.974 Ty
    3.957 Ty
    tps=

    3.33x10-31
    s*
    0.52839
    0.04875
    2.935x1036

    1.59092x1026
    3.7621x1028
    8.89626x1030

    R1(n)=[n-1]n1RH/
    [n-1+n1]

    =½n1RH=
    1.873x1028

    R1E=[n-1]RH
    =n1RH
    =3.7461x1028

    R1P=
    [n-1+n1]R1E

    =2n1R1E=2n12RH
    =1.7567x1031

    λps=10-22
    1.0000x10-22
    5.7636x10-18

    H=1.796x10-5 Ho
    H'= -
    -3.6074x10-5 Ho2
    -1.8035x10-5 Ho2
    H=2.1325x10-3 Ho
    H'=Ho/n1=0.2475
    -7.9967x10-3 Ho2
    -1.8189x10-5 Ho2

    H=fps
    H'=fps
    =-2.2068x10101 Ho2
    =-9x1060

    -0.9979
    470.944


    2


    4.6042x1052
    2.1719x10-53

    1.78830x10-5 c
    -8.5201x10-17

    0.2500 c
    -6.00624x10-13


    c
    -1.9547x10-14
    0.05536
    0.00071
    0.05607

    0.04535
    0.31978
    0.36513

    0.02803
    0.97197
    1

    0.94393
    7.9620x10-12
    5.0047x10-38
    3.2259x10-12
    0.63487
    -6.0005x10-13
    -3.2037x10-41
    -2.0650x10-15

    0
    2.01522x1085
    2.01522x10107

    1.2990x10133

    -
    10,429.5
    6,445.775




    n=255.5865
    =[1]+n1+20.1145↩

    =[1+n1]+20.1145↪
    Λ2=0 from +/-

    1st Λ2 Root

    0.996103
    0.520565
    (122.058)

    3.5355x10-4
    (20.3773)

    1.5189x10-5
    0.2636
    52.5342

    4.313 Ty
    4.296 Ty
    0.339 Ty

    0.51758
    0.04680
    0.2175

    1.5914x1026
    4.0834x1028
    1.0478x1031
    1.9501x1028
    4.0675x1028
    1.9892x1031

    3.2125x1027
    3.2136x1027
    1.8529x1032


    H=1.5249x10-5 Ho
    H'= -
    -3.0616x10-5 Ho2
    - 1.5308x10-5 Ho2
    H=1.8832x10-3 Ho
    H'=0.2708
    Ho/(n1-20.1145)
    -6.8194x10-3 Ho2
    -1.5429x10-5 Ho2

    H=0.0497 Ho
    H'=2.8855
    Ho/[20.1145]
    -284.909 Ho2
    -2.4716x10-3 Ho2


    -0.9980
    511.173

    -0.5395
    2.1716


    1431.704
    6.9798x10-4


    1.5169x10-5 c
    -6.6693x10-17

    0.2299 c
    -5.2952x10-13


    0.9993 c
    -1.9527x10-14



    0.0553575
    0.0006523
    0.0560098

    0.0472649
    0.2210760
    0.2764335

    0.028034
    0.971976
    1

    0.9439902
    7.9573x10-12
    5.0002x10-38
    3.2230x10-12
    0.7235665
    -5.2899x10-13
    -2.7126x10-41
    -1.7485x10-15
    0

    0
    1st Λ2 Root +/-
    0
    0

    -
    10,869.04
    6446.86



    n=332.593=n1√2+1
    =[1]+n1+97.121↩
    BM∩DM Intersect
    ΩBM=constant
    k=1
    =[1+n1]+97.121↪
    0.997002
    0.585786
    (137.350)
    1.6822x10-3
    (96.9576)

    8.9860x10-6
    0.1900
    23.3711
    5.613 Ty
    5.596 Ty
    1.639 Ty
    0.48439
    0.04130
    0.06682
    1.5929x1026
    5.3138x1028
    1.7726x1031
    2.1917x1028
    5.2818x1028
    2.9846x1031

    1.5491x1028
    1.5517x1028
    8.9584x1032
    H=9.0130x10-6 Ho
    H'= -
    -1.8080x10-5 Ho2
    -9.0411x10-6 Ho2
    H=1.2492x10-3 Ho
    H'=0.4226
    Ho/([n1-97.121]
    -4.0820x10-3 Ho2
    -9.0947x10-6 Ho2

    H=0.010279 Ho
    H'=0.5976
    Ho/[97.121]
    -9.1759 Ho2
    -1.0602x10-4 Ho2

    -0.9985
    665.186

    -0.6464
    2.82842


    296.724
    0.00336

    8.9860x10-6 c
    -3.0348x10-17

    0.1716 c
    -3.4148x10-13


    0.9966 c
    -1.9449x10-14


    0.0553575
    0.0005008
    0.0558583

    0.0553575
    0.2200396
    0.2753971
    BM∩DM
    Saturation
    BM∩DM
    Intersect

    ΩBM=constant
    k=1

    0.02805
    0.97195
    1

    0.9441417
    7.9423x10-12
    4.9860x10-38
    3.2139x10-12
    0.7246029
    -3.4106x10-13
    -1.5562x10-41
    -1.0031x10-15

    0
    -1.8609x10-14
    -1.2013x10-42
    -7.7433x10-17

    -
    12,730.0
    6,451.0



    n=486.7205
    =[1]+2n1
    +16.7765↪
    n=[1+n1]

    +251.2485↪
    Λ2 = Minimum DE

    0.997950
    0.674431
    (158.135)

    4.3403x10-3
    (250.158)

    4.2041x10-6
    0.1123
    14.1625

    8.214 Ty
    8.197 Ty
    4.240 Ty

    0.44019
    0.03499
    0.03280

    1.5944x1026
    7.7762x1028
    3.7926x1031
    2.5265x1028
    7.7602x1028
    3.7693x1031

    3.9967x1028
    4.0141x1028
    2.3237x1033




    H=4.2126x10-6 Ho
    H'= -
    -8.4425x10-6 Ho2
    -4.2212x10-6 Ho2
    H=6.7028x10-4 Ho
    H'=3.4596
    Ho/[16.7765]
    -1.9350x10-3 Ho2
    -4.2386x10-6 Ho2

    H=3.9628x10-3 Ho
    H'=0.2310
    Ho/[251.2485]
    -1.3737 Ho2
    -1.5841x10-5 Ho2


    -0.9990
    973.441

    -0.7586
    4.14310


    113.700
    0.00872


    4.2040x10-6 c
    -9.7112x10-18

    0.1060 c
    -1.6581x10-13


    0.9913 c
    -1.9294x10-14
    0.0553575
    0.0003420
    0.0556995

    0.0553575
    0.1250950
    0.1804525

    0.028088
    0.971912
    1

    0.9443005
    7.9274x10-12
    4.9720x10-38
    3.2049x10-12
    0.8195475
    -1.6549x10-13
    -6.5503x10-42
    -4.2222x10-16

    0
    -1.9168x10-14
    Λ2 Minimum
    -4.7959x10-43
    -3.0913x10-17

    -
    17,466.4
    6,459.3




    n=1534.725
    =[1]+6n1+126.893↪
    DM Saturation BM

    k=1
    =[1+n1]+1,299.253↪

    0.999349
    0.867395
    (203.380)

    0.022045
    (1,270.61)

    4.24x10-7
    0.0177
    5.6983

    25.900 Ty
    25.883 Ty
    21.926 Ty

    0.33010
    0.02314
    0.00965

    1.5966x1026
    2.4520x1029
    3.7656x1032
    3.2493x1028
    2.4504x1029
    4.3328x1032

    2.0300x1029
    2.0758x1029
    1.2234x1034

    H=4.2428x10-7 Ho
    H'= -
    -8.4912x10-7 Ho2
    -4.2456x10-7 Ho2
    H=8.6460x10-5 Ho
    H'=0.4574
    Ho/[126.893]
    -1.9848x10-4 Ho2
    -4.2511x10-7 Ho2

    H=7.5271x10-4 Ho
    H'=0.04467
    Ho/[1299.253]
    -0.05196 Ho2
    -5.9240x10-7 Ho2


    -0.99967
    3,069.45

    -0.92356
    13.0824


    21.1848
    0.04508


    4.2456x10-7 c
    -3.1106x10-19

    0.0176 c
    -1.1204x10-14


    0.956395 c
    -1.8283x10-14



    0.0553575
    0.0001083
    0.0554658

    0.0553575
    0.0294680
    0.0848255

    0.028336
    0.971664
    1

    0.9445342
    7.9056x10-12
    4.9515x10-38
    3.1916x10-12
    0.9151745
    -1.1013x10-14
    -3.3894x10-43
    -2.1847x10-17

    0
    -1.8278x10-14
    -9.0040x10-44
    -5.8038x10-18


    -
    150,072.9
    6,516.1






    n=7,161.518
    =[1]+30n1
    +126.352↪

    Λ1=0 from -/+
    2nd Λ1 Root

    =[1+n1]
    +6,925.758↪



    0.999860
    0.968293
    (227.038)

    0.107277
    (6,183.04)

    1.949x10-8
    0.0010058
    1.9749

    120.858 Ty
    120.842 Ty
    116.884 Ty

    0.22454
    0.01490
    0.00288

    1.5975x1026
    1.1442x1030
    8.1952x1033
    3.6273x1028
    1.1440x1030
    8.4600x1033

    9.8785x1029
    1.1066x1030
    7.1674x1034

    H=1.9495x10-8 Ho
    H'= -
    -3.8996x10-8 Ho2
    -1.9498x10-8 Ho2
    H=4.4280x10-6 Ho
    H'=0.4594
    Ho/[126.352]
    -9.1438x10-6 Ho2
    -1.9503x10-8 Ho2

    H=1.2889x10-4 Ho
    H'=8.3803x10-3
    Ho/[6,925.758]
    -1.9242x10-3 Ho2
    -2.0846x10-8 Ho2



    -0.99993
    14,323.0

    -0.98363
    61.0778


    3.16083
    0.24034


    1.9493x10-8 c
    -3.0661x10-21

    0.0010 c
    -1.5316x10-16


    0.7970 c
    -1.3907x10-14

    0.0553575
    0.0000232
    0.0553807

    0.0553575
    0.0056181
    0.0609756
    0.0553575

    0.02970
    0.97030
    1

    0.9446193
    7.8967x10-12
    4.9431x10-38
    3.1863x10-12
    0.9390244
    0
    2nd Λ1 Root -/+
    0
    0

    0
    -1.3907x10-14
    -1.4078x10-44
    -9.0744x10-19

    -
    1.5543x1010
    6,829.5


    n=29,053.485
    =[1]+n1+½n1n2
    =1+123n1
    +212.476↩

    =[1+n1]
    +28,818.0↪
    k=2 DE Initiation
    0.999966
    0.991994
    (232.595)
    0.333332
    (19,212.0)
    1.18x10-9
    6.4098x10-5
    0.61245
    490.310 Ty
    490.293 Ty
    486.336 Ty
    0.15821
    0.01037
    0.00114
    1.59762x1026
    4.64180x1030
    1.34865x1035
    3.71611x1028
    4.64164x1030
    1.35940x1035

    3.06946x1030
    4.60418x1030
    3.98051x1035
    1.1145x10-9 Ho
    H'= -
    -2.3694x10-9 Ho2
    -1.1847x10-9 Ho2
    H=2.7557x10-7 Ho
    H'=2.6387
    Ho/[n1-212.476]
    -5.5558x10-7 Ho2
    -1.1848x10-9 Ho2

    2.3134x10-5 Ho
    H'=0.002014
    Ho/[28,818.0]
    -1.2338x10-4 Ho2
    -1.2041x10-9 Ho2



    -0.999983
    58,104.97

    -0.99596
    247.812


    0
    1
    k=2 DE
    Initiation

    1.1846x10-9 c
    -4.5935x10-23

    6.4096x10-5 c
    -2.4657x10-18


    0.4444 c
    -5.7918x10-15
    0.0553575
    0.0000057
    0.0553632

    0.0553575
    0.0013512
    0.0567087


    0.0356547
    0.9270302
    0.9626849

    0.9446368
    7.8957x10-12
    4.9422x10-38
    3.1856x10-12
    0.9432913
    1.4340x10-16
    3.8578x10-45
    2.4867x10-19

    0.0373151
    -5.7918x10-15
    -1.8488x10-45
    -1.1917x10-19
    -
    5.0594x1029
    8,199.1



    n=51,941.9
    =[1]+221n1
    +122.588↩

    Λ1= Maximum DE
    Asymptote:
    Λ1⇒ GoMo/n12RH2
    =1.436041x10-16

    =[1+n1]
    +51,706.428

    0.999981
    0.995506
    (233.418)

    0.472884
    (27,255.3)

    3.7x10-10
    2.01955x10-5
    0.33023

    876.577 Ty
    876.560 Ty
    872.603 Ty

    0.13682
    0.00896
    0.00085

    1.59764x1026
    8.30342x1030
    4.31304x1035
    3.72927x1028
    8.29847x1030
    4.32976x1035

    4.35451x1030
    8.26101x1030
    9.03281x1035


    H=3.7064x-10 Ho
    H'= -
    -7.4130x10-10 Ho2
    -3.7065x10-10 Ho2
    H=2.7557x10-7 Ho
    H'=0.5188
    Ho/[n1-122.588]
    -1.7382x10-7 Ho2
    -3.7066x10-10 Ho2

    H=1.0194x10-5 Ho
    H'=0.001122
    Ho/[51,706.428]
    -6.6466x10-6 Ho2
    -3.7403x10-10 Ho2



    -0.999990
    103,883.81


    -0.99774
    443.046


    -0.44265
    1.79420

    3.7064x10-10 c
    -8.0391x10-24


    2.0195x10-5 c
    -4.3608x10-19


    0.2779 c
    -2.8264x10-15


    0.0553575
    0.0000032
    0.0553607


    0.0553575
    0.0007531
    0.0561106


    0.0431628
    0.3650112
    0.4081740

    0.9446393
    7.8953x10-12
    4.9418x10-38
    3.1854x10-12

    0.9438894
    1.4447x10-16
    Λ1= Maximum DE
    3.8739x10-45
    2.4970x10-19

    0.591826
    -2.8264x10-15
    -6.4907x10-46
    -4.1838x10-20

    -
    1.2729x1050


    9,925.7

    n=57,636.03=n1n2
    =234.472x245.813
    =[1]+245n1
    +189.491↩↪

    =[1+n1]
    +57,400.565↪



    Quantum Tunnel
    n1n2

    k=1 to k=2
    0.999983
    0.995948
    (233.522)
    0.498976
    (28,759.1)
    ~3.0x10-10
    1.642x10-5
    0.29241
    972.68 Ty
    972.66 Ty
    968.70 Ty
    0.133305
    0.008723
    0.000787
    1.59765x1026
    9.20837x1030
    5.30743x1035
    3.73092x1028
    9.20837x1030
    5.32884x1035

    4.59477x1030
    9.17075x1030
    1.05497x1036

    H=3.0103x10-10 Ho
    H'= -
    -6.0206x10-10 Ho2
    -3.0103x10-10 Ho2
    H=7.0300x10-8 Ho
    H'=1.2903
    Ho/[n1-189.491]
    =1.262

    Ho**=Ho/n1n2
    =0.001007

    -1.4117x10-7 Ho2
    -3.0104x10-10 Ho2

    H=8.7286x10-6 Ho
    H'=0.001011
    Ho/[57,400.565]
    -3.2790x10-5 Ho2
    -3.0351x10-10 Ho2

    -0.999991
    115,272.1

    -0.99797
    491.616


    -0.49794
    1.99182

    3.0102x10-10 c
    -5.8841x10-24

    1.6417x10-5 c
    -3.1961x10-19


    0.2510 c
    -2.4585x10-15
    0.0553575
    0.0000029
    0.0553604

    0.0553575
    0.0006784
    0.0560359

    0.0452643
    0.3190851
    0.3647094

    0.9446396
    7.8962x10-12

    4.9418x10-38
    3.1854x10-12
    0.9439641
    1.4446x10-16
    3.8719x10-45
    2.4957x10-19

    0.6352906
    -2.4585x10-15
    -5.3506x10-46
    -3.4489x10-20

    -
    1.5138x1055
    10,409.0


    n=57,637.03
    =[1]+n1n2
    MH*=n1MH
    =1.5172x1055

    =[1+n1]
    +57,401.565↪

    0.999983
    0.995948
    (233.522)

    0.498980
    (28,759.3)
    ~3.0x10-10
    1.642x10-5
    0.29240
    972.69 Ty
    972.67 Ty
    968.71 Ty

    0.133305
    0.008723
    0.000787


    1.59765x1026
    9.20853x1030
    5.30761x1035
    3.73092x1028
    9.20837x1030
    5.32893x1035

    4.59481x1030
    9.17091x1030
    1.05501x1036
    H=3.0102x10-10 Ho
    H'= -
    -6.0204x10-10 Ho2
    -3.0102x10-10 Ho2
    H=7.0297x10-8 Ho
    H'= -
    -1.4117x10-7 Ho2
    -3.0103x10-10 Ho2

    H=8.7283x10-6 Ho
    H'=0.001011
    Ho/[57,401.565]
    -3.2789x10-5 Ho2
    -3.0350x10-10 Ho2

    -0.999991
    115,274.1


    -0.99797
    491.624


    -0.49796
    1.99186



    3.0101x10-10 c
    -5.8838x10-24


    1.6416x10-5 c
    -3.1959x10-19


    0.2510 c
    -2.4584x10-15
    0.0553575
    0.0000029
    0.0553604


    0.0553575
    0.0006784
    0.0560359


    0.0452647
    0.3190784
    0.3643431

    0.9446396
    7.8952x10-12
    4.9418x10-38
    3.1854x10-12
    0.9439641
    1.4446x10-16
    3.8718x10-45
    2.4957x10-19

    0.6356569
    -2.4584x10-15
    -5.3504x10-46
    -3.4487x10-20

    -
    MH*=n1MH
    =1.5172x1055

    10,409.1
    k=3 initiated
    n=nps+1+n1+n1n2
    n3=257.252
    4th Instanton
    from 4th Inflaton
    RE3=n1n2n3RH



    Scalefactor
    {n1n2n3}

    a3=
    [n-1-n1-n1n2]
    /[n-1-n1-n1n2+
    n1n2n3]
    a3<0 for n<
    [1+n1+n1n2]+
    n1n2n3/
    (n1n2n3-1)=
    57,871.509+
    14,827,044.63/
    14,827,043.63


    lim
    {1+n1+n1n2+1+
    =57,872.509+}

    Redshift z3
    n=1+n1+
    n1n2+nps


    [z+1]2 = 1+
    2(n1n2n3)2
    /{n2+2n[n1n2n3
    -1-n1-n1n2]+[1+n1+n1n2][1+n1+n1n2
    -2n1n2n3]}

    =1+n1n2n3/nps

    4.8671x10x1027


    Time t3

    t3=t-
    (1+n1+n1n2)
    /Ho=(n-1-n1-
    n1n2)/Ho



    Temp T34

    18.2
    [n-1-n1-
    n1n2+
    n1n2n3]2/
    {[n1n2n3]2
    (n-1-n1-n1n2)3
    }
    =2.935x1036

    R3=
    n1n2n3RH(
    [n-1-n1-n1n2)/
    [n-1-n1-n1n2+
    n1n2n3]

    ps=10-22

    R3E=[n-1-n1
    -n1n2]RH
    ps


    R3P=[n-1-n1-
    n1n2+
    n1n2n3]R3E

    =[n1n2n3ps
    =1.4827x10-15

    H|dS=
    n1n2n3Ho/{[n-1-n1-n1n2]
    [n-1-n1-n1n2+n1n2n3]}=fps


    H'=Ho/(n-1-n1-n1n2)'=fps

    ||nps+1+n1+n1n2 - n1n2n3+n1n2+n1+1||


    dH/dt|dS=
    -2n1n2n3Ho2([n-1-n1-n1n2+n1n2n3]2
    -¼n12n22n32)/(
    [n-1-n1-n1n2][n-1
    -n1-n1n2+n1n2n3])2

    =-(3n1n2n3/2nps2) Ho2
    =-5.6771x10103 Ho2


    dH/dt|AdS=
    -Ho2/(n-1-n1-n1n2)2

    =-fps2=-9x1060

    qdS=n1n2n3/
    2[n-1-n1-n1n2]-1
    =n1n2n3/
    2nps -1


    qAdS=2[n-
    -n1-n1n2]
    /n1n2n3
    =2nps/
    n1n2n3



    1.184x1055
    8.443x10-56


    V1=cn12n22n32/
    (n-1-n1
    -n1n2+n1n2n3)2
    A1=
    -2cHon12n22n32
    /(n-1-n1-n1n2+n1n2n3)3
    =-2cHo/n1n2n3
    =-7.5985x10-17
    BM-DM
    ΩBM=
    MoYN3/MH

    N3=[n-1-n1-n1n2]/
    n1n2n3

    to BM∩DM ΩDMBM.{[1+1/N3]3-1}
    {1+n1n2n3/
    [n-1-n1-n1n2]}3-1

    after
    saturation


    0.02803
    0.97197
    1




    DE %
    Pressure
    0

    Λ3=GoMo/R32
    -2cHon12n22n32/
    [n-1-n1-n1n2+n1n2n3]3
    =GoMops3-2cHo/n1n2n3
    =2.01522x1085
    Λ3/R3=GoMo/R33
    -2Ho2n1n2n3/
    [n-1-n1-n1n2]
    [n-1-n1-n1n2+n1n2n3]2
    =GoMops3
    -2Hofps/n1n2n3
    =2.01522x10107


    -P33c2/4πGoR3
    =1.2990x10133

    n≥1+nps+n1+n1n2
    =57,871.738



    HyperMass

    MHyper=mH
    Y{[n-1-n1-n1n2]/
    n1n2n3}



    MH***=
    n1n2n3MH
    =9.5940x1059


    mps=
    2.22x10-20

    Y{[n-1-n1-n1n2]/
    (n1n2n3}=
    2πn1n2n3RHps
    =MH*/mH


    mH=6445.775
    3rd Mirror Node

    n=1+n1+n1n2

    =57,871.509
    =[1+n1]+n1n2
    =[1+n1+n1n2]+nps
    ....
    4th Inflaton
    triple
    imaged in

    {nps};{1};{1+n1}
    0.99998272
    0.99596468
    (233.52583)
    0.50000000
    (28,818.08)
    4.2214x10-56
    (nps)

    ~3.0x10-10
    1.628x10-5
    0.29099
    4.8671x
    1027


    976.65 Ty
    976.63 Ty
    972.68 Ty
    tps=
    3.33x10-31
    s*
    0.133170
    0.008714
    0.000785
    2.935x1036
    1.59765x1026
    9.24599x1030
    5.35089x1035

    3.73098x1028
    9.24583x1030
    5.37229x1035


    R2=n1n2RH(n-1-n1)/[n-1-n1+n1n2]
    =½n1n2RH
    =4.60419x1030


    R2E=[n-1-n1]RH
    =[n1n2]RH

    =9.20837x1030

    R2P=[n-1-n1+n1n2]R1E
    =2n1n2R2E

    =2[n1n2]2RH
    =1.06147x1036

    10-22
    1.00000x10-22
    1.48270x10-15
    H=2.9858x10-10 Ho
    H'= -
    -5.9725x10-10 Ho2
    -2.9859x10-10 Ho2
    H=6.9732x10-8 Ho
    H'= -
    -1.4002x10-7 Ho2
    -2.9860x10-10 Ho2

    H=8.6751x10-6 Ho
    H'=Ho/n1n
    2
    =1.0070x10-3
    -3.2532x10-5 Ho2
    -3.0103x10-10 Ho2

    H=fps
    H'=fps
    -5.6771x10103 Ho2
    -9x1060

    -0.999991
    115,743.0


    -0.99797
    493.624



    2


    1.184x1055
    8.443x10-56

    2.9858x10-10 c
    -5.8126x10-24

    1.6284x10-5 c
    -3.1574x10-19


    0.2500 c
    -2.4434x10-15


    c
    -7.5985x10-17
    0.0553575
    0.0000029
    0.0553604


    0.0553575
    0.0006756
    0.0560331

    0.0453534
    0.3174760
    0.3628294

    0.0280300
    0.9719700
    1


    0.9446396
    7.8952x10-12
    4.9418x10-38
    3.1854x10-12
    0.9439669
    1.4445x10-16
    3.8718x10-45
    2.4957x10-19

    0.6371706
    -2.4434x10-15
    -5.3069x10-46
    -3.4207x10-20

    0
    2.01522x1085
    2.01522x10107
    1.2990x10133
    -
    -
    10,429.5
    6,445.77


    n=58,194.1
    n=[1+n1]+n1n2
    +322.362↩
    n=[1+n1+n1n2]

    +322.362↪

    Λ3=0 from +/-
    1st Λ3 Root

    0.99998282
    0.99598696
    (233.53105)

    0.50139436
    (28,898.50)

    2.1741x10-5
    (322.35526)

    2.9x10-10
    1.610x10-5
    0.28908
    213.466

    982.09 Ty
    982.07 Ty
    978.12 Ty
    5.4402 Ty

    0.132984
    0.008702
    0.000783
    0.027150

    1.59765x1026
    9.29737x1030
    5.41061x1035
    3.73107x1028
    9.29737x1030
    5.43223x1035

    4.61704x1030
    9.25991x1030
    1.07040x1036

    5.15019x1028
    5.15033x1028
    7.63659x1035




    H=2.9528x10-10 Ho
    H'= -
    -5.9057x10-10 Ho2
    -2.9529x10-10 Ho2
    H=6.8961x10-8 Ho
    H'= -
    -1.3848x10-7 Ho2
    -2.9529x10-10 Ho2

    H=8.6028x10-6 Ho
    H'=0.001013
    Ho/[n1n2-322.362]

    -3.2183x10-5 Ho2
    -2.9769x10-10 Ho2

    H=0.00310203 Ho
    H'=0.180046
    Ho/[322.362]
    -214.0246 Ho2
    -9.6230x10-6
    Ho2


    -0.999991
    116,388.2

    -0.99799
    496.376


    -0.50278
    2.01119


    22,996.488
    4.348x10-5

    2.9528x10-10 c
    -5.7164x10-24

    1.6104x10-5 c
    -3.1054x10-19


    0.2486 c
    -2.4230x10-15


    0.99996 c
    -7.5980x10-17
    0.0553575
    0.0000029
    0.0553604


    0.0553575
    0.0006718
    0.0560293

    0.0454757
    0.3153031
    0.3607788

    0.0280303
    0.9719697
    1


    0.9446396
    7.8952x10-12
    4.9418x10-38
    3.1854x10-12

    0.9439707
    1.4445x10-16
    3.8716x10-45
    2.4956x10-19

    0.6392212
    -2.4230x10-15
    -5.2479x10-46
    -3.3827x10-20

    0
    1st Λ3 Root +/-
    0
    0
    0

    -
    -
    10,457.6
    6,445.84


    n=67,972.497
    n=[1+n1]+n1n2
    +10,100.759↩
    n=[1+n1+n1n2]
    +10,100.759↪



    Λ3 = Minimum DE

    0.99998529
    0.99656230
    (233.66595)

    0.54028274
    (31,139.88)

    6.8078x10-4
    (10,093.88)

    2.1x10-10
    1.182x10-5
    0.23933
    37.320

    1,147.11 Ty
    1,147.09 Ty
    1,143.14 Ty
    170.461 Ty

    0.127920
    0.008368
    0.000725
    0.002051

    1.59765x1026
    1.08598x1031
    7.38179x1035
    3.73322x1028
    1.08596x1031
    7.40692x1035

    4.97514x1030
    1.08222x1031
    1.35681x1036

    1.61267x1030
    1.61377x1030
    2.39438x1037




    H=2.1643x10-10 Ho
    H'= -
    -4.3288x10-10 Ho2
    -2.1644x10-10 Ho2
    H=5.0576x10-8 Ho
    H'= -
    -1.0150x10-7 Ho2
    -2.1644x10-10 Ho2

    H=6.7868x10-6 Ho
    H'=0.001221
    Ho/[n1n2-10,100.759]
    -2.3796x10-5 Ho2
    -2.1795x10-10 Ho2

    H=9.8935x10-5 Ho
    H'=0.005746
    Ho/[10,100.759]
    -0.218090 Ho2
    -9.8015x10-9
    Ho2


    -0.999993
    135,945.00

    -0.99828
    579.784


    -0.5746
    2.35050


    732.957
    1.362x10-3


    2.1643x10-10 c
    -3.5873x10-24

    1.1818x10-5 c
    -1.9521x10-19


    0.2113 c
    -1.8992x10-15


    0.99864 c
    -7.5830x10-17
    0.0553575
    0.0000024
    0.0553599


    0.0553575
    0.0005749
    0.0559324

    0.0493442
    0.2635322
    0.3128764

    0.0280392
    0.9719608
    1


    0.9446401
    7.8952x10-12
    4.9418x10-38
    3.1854x10-12

    0.9440676
    1.4440x10-16
    3.8680x10-45
    2.4932x10-19

    0.6871236
    -1.8992x10-15
    -3.8174x10-46
    -2.4606x10-20

    0
    -7.5753x10-17
    -4.6973x10-47
    -3.0278x10-21

    -
    -
    11,347.2
    6,447.89







    n=81,745.461
    =n1n2√2+1+n1
    =[1+n1]
    +√2.n1n2

    =[1+n1]+n1n2
    +23,873.72↩


    BM∩DM Intersect
    ΩBM=constant
    k=2

    n=[1+n1+n1n2]

    +23,873.722↪
    0.99998777
    0.99713985
    (233.80138)
    0.58578644
    (33,762.54)
    1.6076x10-3
    (23,835.34)

    ~1.5x10-10
    8.180x10-6
    0.18921
    23.931
    1,379.55 Ty
    1,379.53 Ty
    1,375.57 Ty
    402.894 Ty
    0.122153
    0.007966
    0.000665
    0.001076
    1.59766x1026
    1.30603x1031
    1.06763x1036
    3.73539x1028
    1.30601x1031
    1.07065x1036

    5.39416x1030
    1.30227x1031
    1.81205x1036

    3.80811x1030
    3.81425x1030
    5.66451x1037

    H=1.4965x10-10 Ho
    H'= -
    -2.9930x10-10 Ho2
    -1.4965x10-10 Ho2
    H=3.4988x10-8 Ho
    H'= -
    -7.0178x10-8 Ho2
    -1.4965x10-10 Ho2

    H=5.0818x10-6 Ho
    H'=0.001719
    Ho/[n1n2-23,873.72]
    -1.6606x10-5 Ho2
    -1.5051x10-10 Ho2

    H=4.1820x10-5 Ho
    H'=0.002431
    Ho/[23,873.722]
    -0.03906 Ho2
    -1.7545x10-9 Ho2

    ~-1
    163,490.9

    -0.99857
    697.264


    -0.64645
    2.82843


    309.5306
    3.220x10-3

    1.4964x10-10 c
    -2.0624x10-24

    8.1805x10-6 c
    -1.1242x10-19


    0.1716 c
    -1.3892x10-15


    0.99679 c
    -7.5619x10-17

    0.0553575
    0.0000020
    0.0553595

    0.0553575
    0.0004777
    0.0558352

    0.0553575
    0.2200391
    0.2753966
    BM∩DM Intersect
    BM∩DM Intersect

    ΩBM=constant
    k=2

    0.0280517
    0.9719483
    1

    0.9446405
    7.8951x10-12
    4.9417x10-38
    3.1853x10-12
    0.9441648
    1.4432x10-16
    3.8635x10-45
    2.4903x10-19

    0.7246034
    -1.3892x10-15
    -2.5754x10-46
    -1.6600x10-20

    0
    -7.5605x10-17
    -1.9854x10-47
    -1.2797x10-21
    -
    -
    12,730.0
    6,450.77








    n=337,244.12
    =[1+n1+n1n2]
    +279,372.61
    =[57,871.51]
    +279,372.61
    n=[1+n1]
    +5n1n2
    +48,827.32↩

    DM Saturation BM
    k=2

    n=[1+n1+n1n2]

    +279,372.61↪

    0.99999703
    0.99930522
    (234.30909)

    0.85395411
    (49,218.73)

    0.01849362
    (274,205.8)

    ~0
    4.827x10-7
    0.02156
    6.3197

    5,691.37 Ty
    5,691.35 Ty
    5,687.39 Ty
    4,714.72 Ty

    0.085710
    0.005599
    0.000386
    0.000172


    1.59767x1026
    5.38807x1031
    1.81710x1037
    3.74350x1028
    5.38805x1031
    1.81834x1037

    7.86356x1030
    5.38430x1031
    2.12489x1037

    4.38092x1031
    4.46346x1031
    6.74269x1038





    H=8.7925x10-12 Ho
    H'= -
    -1.7585x10-11 Ho2
    -8.7925x10-12 Ho2
    H=2.0602x10-9 Ho
    H'= -
    -4.1232x10-9 Ho2
    -8.7925x10-12 Ho2

    H=4.3336x10-7 Ho
    H'=0.006589
    Ho/[n1n2-48,827.32]
    -1.0095x10-6 Ho2
    -8.8048x10-12 Ho2

    H=3.5133x10-6 Ho
    H'=0.000208
    Ho/[279,372.61]
    -0.0002884 Ho2
    -1.2812x10-11
    Ho2


    -0.999999
    674,488.48

    -0.999652
    2,876.62


    -0.914488
    11.69433


    25.53635
    0.037684



    8.7924x10-12 c
    -2.9373x10-26


    4.8272x10-7 c
    -1.6115x10-21


    0.02133 c
    -6.0891x10-17


    0.96335 c
    -7.1847x10-17
    0.0553575
    0.0000005
    0.0553580

    0.0553575
    0.0001155
    0.0554730

    0.0553575
    0.0335366
    0.0888941

    0.0282853
    0.9717147
    1


    0.9446420
    7.8950x10-12
    4.9416x10-38
    3.1852x10-12

    0.9445270
    1.4380x10-16
    3.8414x10-45
    2.4761x10-19

    0.9111059
    -6.0888x10-17
    -7.7430x10-48
    -4.9910x10-22

    0
    -7.1847x10-17
    -1.6400x10-48
    -1.0571x10-22
    -
    -
    107,463.3
    6,504.48


    n=7,471,394.054
    n=[1+n1]
    +129n1n2
    +36,080.302↩


    n=[1+n1+n1n2]
    +7,413,522.54↪
    k=3 DE Initiation

    ~1
    0.99996862
    (234.46464)

    0.99234456
    (57,195.03)

    0.33333333
    (4,942,348.2)


    ~0
    9.8x10-10
    5.8608x10-5
    0.61245

    126.088 Py
    126.088 Py
    126.084 Py
    125.111 Py

    0.039506
    0.002580
    0.000165
    0.000018

    1.59768x1026
    1.19369x1033
    8.91850x1039
    3.74598x1028
    1.19369x1033
    8.91878x1039

    9.13791x1030
    1.19365x1033
    8.98674x1039

    7.89627x1032
    1.18444x1033
    2.63426x1040



    H=1.7914x10-14 Ho
    H'= -
    -3.5828x10-14 Ho2
    -1.7914x10-14 Ho2
    H=4.2002x10-12 Ho
    H'= -
    -8.4007x10-12 Ho2
    -1.7914x10-14 Ho2

    H=1.0247x10-9 Ho
    H'=0.002693
    Ho/[n1n2-36,080.302]
    -2.0651x10-9 Ho2
    -1.7915x10-14 Ho2

    H=8.9926x10-8 Ho
    H'=7.8289x10-6
    Ho/[7,413,522.54]
    -4.7960x10-7 Ho2
    -1.8195x10-14
    Ho2


    ~-1
    1.4942x106

    -0.9999843
    63,729.51


    -0.996143
    259.252


    0
    1
    k=3 DE
    Initiation

    1.7914x10-14 c
    -2.7013x10-30


    9.8481x10-10 c
    -1.4850x10-25


    5.8606x10-5 c
    -8.7000x10-21


    0.44444 c
    -2.2514x10-17

    0.0553575
    0.0000000
    0.0553575

    0.0553575
    0.0000052
    0.0553627

    0.0553575
    0.0012911
    0.0566486

    0.0356547
    0.9270222
    0.9626769


    0.9446425
    7.8949x10-12
    4.9415x10-38
    3.1852x10-12

    0.9446373
    1.4361x10-16
    3.8338x10-45
    2.4712x10-19

    0.9433514
    -6.2866x10-21
    -6.8797x10-52
    -4.4345x10-26

    0.0373231
    -2.2514x10-17
    -2.8512x10-50
    -1.8378x10-24
    -
    -
    7.9343x1030
    8,199.15
    n=11,538,294.3

    n=[1+n1]
    +200n1n2
    +10,811.4↪


    Λ2=0 from -/+

    2nd Λ2 Root -/+

    =[1+n1+n1n2]
    +11,480,422.79↪

    ~1
    0.99997968
    (234.46724)

    0.99502951
    (57,349.79)

    0.43639407
    (6,470,434.3)


    ~0
    4.1x10-10
    2.4706x10-5
    0.38962

    194.721 Py
    194.721 Py
    194.718 Py
    193.745 Py

    0.035439
    0.002314
    0.000148
    0.000014


    1.59768x1026
    1.84344x1033
    2.12702x1040
    3.74603x1028
    1.84344x1033
    2.12706x1040

    9.16264x1030
    1.84341x1033
    2.13756x1040

    1.03377x1033
    1.83420x1033
    4.82532x1040


    H=7.5113x10-15 Ho
    H'= -
    -1.5023x10-14 Ho2
    -7.5113x10-15 Ho2
    H=1.7612x10-12 Ho
    H'= -
    -3.5224x10-12 Ho2
    -7.5113x10-15 Ho2

    H=4.3079x10-10 Ho
    H'=0.005368
    Ho/[10,811.4]
    -8.6588x10-10 Ho2
    -7.5116x10-15 Ho2

    H=4.9093x10-8 Ho
    H'=5.0556x10-6
    Ho/[11,480,422.79]
    -2.0713x10-7 Ho2
    -7.5872x10-15
    Ho2


    ~-1
    2.3077x107

    -0.999990
    98,419.38


    -0.997502
    400.375


    -0.354247
    1.548579



    7.5113x10-15 c
    -7.3341x10-31


    4.1293x10-10 c
    -4.0319x10-26


    2.4706x10-5 c
    -2.4004x10-21


    0.31765 c
    -1.3604x10-17

    0.0553575
    0.0000000
    0.0553575

    0.0553575
    0.0000034
    0.0553609

    0.0553575
    0.0008337
    0.0561912


    0.0406855
    0.4488717
    0.4895572


    0.9446425
    7.8949x10-12
    4.9415x10-38
    3.1852x10-12
    0.9446391
    1.4361x10-16
    3.8336x10-45
    2.4711x10-19

    0.9438088
    0
    2nd Λ2 Root -/+
    0
    0

    0.5104428
    -1.3604x10-17
    -1.3160x10-50
    -8.4824x10-25
    -
    -
    4.4257x1045
    9,356.04



    n=14,827,044.63
    =n1n2n3
    =234.472x245.813
    x257.252

    [1+n1]+257n1n2
    +14,288.86↩↪

    =[1+n1+n1n2]
    +14,769,172.9↪

    Quantum Tunnel
    k=2 to k=3

    ~1
    0.99998419
    (234.46829)

    0.99612775
    (57,413.08)

    0.49902231
    (7,399,026.1)


    ~0
    2.5x10-10
    1.4994x10-5
    0.29234

    250.223 Py
    250.223 Py
    250.219 Py
    249.246 Py

    0.033285
    0.002174
    0.000139
    0.000012

    1.59768x1026
    2.36888x1033
    3.51235x1040
    3.74604x1028
    2.36888x1033
    3.51240x1040

    9.17275x1030
    2.36881x1033
    3.52584x1040

    1.18212x1033
    2.35963x1033
    6.98363x1040



    H=4.5487x10-15 Ho
    H'= -
    -9.0975x10-15 Ho2
    -4.5487x10-15 Ho2
    H=1.0665x10-12 Ho
    H'= -
    -2.1331x10-12 Ho2
    -4.5487x10-15 Ho2

    H=2.6117x10-10 Ho
    H'=0.001339
    Ho/[n1n2-14,288.86]
    -5.2436x10-10 Ho2
    -4.5489x10-15 Ho2

    H=3.3920x10-8 Ho
    H'=3.9298x10-6
    Ho/[14,769,172.9]
    -1.2742x10-7 Ho2
    -4.5845x10-15
    Ho2


    ~-1
    2.9654x107

    -0.999992
    126,471.77


    -0.998056
    514.496


    -0.498041
    1.992194


    4.5487x10-15 c
    -3.4564x10-31


    2.5007x10-10 c
    -1.9001x10-26


    1.4994x10-5 c
    -1.1350x10-21


    0.25098 c
    -9.5540x10-18



    0.0553575
    0.0000000
    0.0553575

    0.0553575

    0.0000026
    0.0553601

    0.0553575
    0.0006481
    0.0560056


    0.0452684
    0.3190115
    0.3642799



    0.9446425
    7.8949x10-12
    4.9415x10-38
    3.1852x10-12

    0.9446399
    1.4361x10-16
    3.8336x10-45
    2.4711x10-19

    0.9439944
    1.2601x10-21
    1.3738x10-52
    8.8550x10-27

    0.6357201
    -9.5540x10-18
    -8.0821x10-51
    -5.2095x10-25
    -
    -
    4.4257x1045
    10,409.91



    n=14,827,185.4
    =[1+n1]+n1n2n3

    MH**=n1n2MH
    =3.7294x1057


    =[1+n1+n1n2]
    +14,769,313.7↪

    ~1
    0.99998419
    (234.46829)

    0.99612781
    (57,413.09)

    0.49902469
    (7,399,061.4)

    ~0
    2.5x10-10
    1.4994x10-5
    0.29234

    250.225 Py
    250.225 Py
    250.221 Py
    249.249 Py


    0.033285
    0.002174
    0.000139
    0.000012

    1.59768x1026
    2.36890x1033
    3.51242x1040
    3.74604x1028
    2.36890x1033
    3.51247x1040

    9.17275x1030
    2.36886x1033
    3.52596x1940

    1.18213x1033
    2.35966x1033
    6.98373x1040
    H=4.5487x10-15 Ho
    H'= -
    -9.0973x10-15 Ho2
    -4.5487x10-15 Ho2
    H=1.0665x10-12 Ho
    H'= -
    -2.1331x10-12 Ho2
    -4.5487x10-15 Ho2

    H=2.6116x10-10 Ho
    H'= -
    -5.2435x10-10 Ho2
    -4.5488x10-15 Ho2

    H=3.3920x10-8 Ho
    H'=3.9298x10-6
    Ho/[14,769,313.7]
    -1.2742x10-7 Ho2
    -4.5844x10-15
    Ho2

    ~-1
    2.9655x107


    -0.999992
    126,472.97


    -0.998056
    514.501


    -0.498046
    1.992213

    4.5486x10-15 c
    -3.4563x10-31


    2.5006x10-10 c
    -1.9001x10-26


    1.4994x10-5 c
    -1.1349x10-21


    0.25098 c
    -9.5538x10-18

    0.0553575
    0.0000000
    0.0553575

    0.0553575
    0.0000026
    0.0553601

    0.0553575
    0.0006481
    0.0560056


    0.0452686
    0.3168837
    0.3621523

    0.9446425
    7.8949x10-12
    4.9415x10-38
    3.1852x10-12
    0.9446399
    1.4361x10-16
    3.8336x10-45
    2.4711x10-19

    0.9439944
    1.2602x10-21
    1.3739x10-52
    8.8557x10-27

    0.6378477
    -9.5538x10-18
    -8.0819x10-51
    -5.2094x10-25
    -
    -
    -
    MH**=n1n2MH
    =3.7294x1057
    10,409.96


    n=2.10264794x107
    n=[1+n1+n1n2]
    +√2.n1n2n3

    =[1+n1+n1n2]
    +n1n2n3
    +6,141,563.032↩


    BM∩DM Intersect
    ΩBM=constant
    k=3

    ~1
    0.99998885
    (234.46939)

    0.99726637
    (57,478.71)

    0.58578644
    (8,685,481.7)


    ~0
    1.2x10-10
    7.4730x10-6
    0.18921

    354.845 Py
    354.845 Py
    354.841 Py
    353.868 Py

    0.030502
    0.001992
    0.000127
    0.000010

    1.59768x1026
    3.35935x1033
    7.06353x1040
    3.74606x1028
    3.35935x1033
    7.06361x1040

    9.18323x1030
    3.35931x1033
    7.08273x1040

    1.38766x1033
    3.35010x1033
    1.19919x1041


    H=2.2619x10-15 Ho
    H'= -
    -4.5237x10-15 Ho2
    -2.2619x10-15 Ho2
    H=5.3034x10-13 Ho
    H'= -
    -1.0607x10-12 Ho2
    -2.2619x10-15 Ho2

    H=1.3001x10-10 Ho
    H'= -
    -2.6074x10-10 Ho2
    -2.2619x10-15 Ho2

    H=1.9754x10-8 Ho
    H'=6.6824x10-6
    Ho/[n1n2n3-
    6,141,563.032]

    -6.4551x10-8 Ho2
    -2.2744x10-15
    Ho2


    ~-1
    4.2054x107

    -0.999994
    179,351.74


    -0.998629
    729.619


    -0.646447
    2.828427


    2.2619x10-15 c
    -1.2119x10-31

    1.2435x10-10 c
    -6.6627x10-27


    7.4729x10-6 c
    -3.9932x10-22


    0.17157 c
    -5.4001x10-18

    0.0553575
    0.0000000
    0.0553575

    0.0553575
    0.0000019
    0.0553594

    0.0553575
    0.0004565
    0.0558140


    0.0553575
    0.2200391
    0.2753966


    0.9446425
    7.8949x10-12
    4.9415x10-38
    3.1852x10-12

    0.9446406
    1.4361x10-16
    3.8336x10-45
    2.4710x10-19

    0.9441860
    1.9903x10-21
    2.1674x10-52
    1.3970x10-26

    0.7246034
    -5.4001x10-18
    -3.8915x10-51
    -2.5084x10-25

    -
    -
    -
    12,730.0




    n=2.0230105x108
    =[1+n1]
    +3,509n1n2
    +36,419.7

    Λ2 = Maximum DE
    Asymptote
    Λ2∞ = GoMo/
    n12n22RH2
    =
    2.3766059x10-21 (m/s2)*


    n=[1+n1+n1n2]
    +13n1n2n3
    +9,491,598.0↩

    ~1
    0.99999884
    (234.47173)

    0.99971518
    (57,619.85)

    0.93169471
    (13,814,279.0)


    ~0
    ~0
    8.112x10-8
    4.6765x10-3

    3,414.05 Py
    3,414.05 Py
    3,414.05 Py
    3,413.08 Py

    0.017319
    0.001131
    0.000072
    0.000005

    1.59768x1026
    3.23211x1034
    6.53860x1042
    3.74610x1028
    3.23211x1034
    6.53861x1042

    9.20578x1030
    3.23211x1034
    6.54045x1042

    2.20707x1033
    3.23119x1034
    7.01395x1042



    H=2.4435x10-17 Ho
    H'= -
    -4.8869x10-17 Ho2
    -2.4435x10-17 Ho2
    H=5.7292x10-15 Ho
    H'= -
    -1.1458x10-14 Ho2
    -2.4435x10-17 Ho2

    H=1.4079x10-12 Ho
    H'= -
    -2.8166x10-12 Ho2
    -2.4435x10-17 Ho2

    H=3.3774x10-10 Ho
    H'=1.0878x10-5
    Ho/[n1n2n3-
    9,491,598.0]

    -7.2415x10-10 Ho2
    -2.4449x10-17
    Ho2


    ~-1
    4.0469x108

    -0.999999
    1.7256x106


    -0.999858
    7,019.91


    -0.963344
    27.280



    2.4435x10-17 c
    -1.3608x10-34

    1.3433x10-12 c
    -7.4812x10-30


    8.1124x10-8 c
    -4.5166x10-25


    4.6656x10-3 c
    -2.4215x10-20


    0.0553575
    0.0000000
    0.0553575

    0.0553575

    0.0000002
    0.0553577

    0.0553575
    0.0000473
    0.0554048


    0.0553575
    0.0130897
    0.0684472


    0.9446425
    7.8949x10-12
    4.9415x10-38
    3.1852x10-12

    0.9446423
    1.4360x10-16
    3.8334x10-45
    2.4709x10-19

    0.9445952
    2.3775x10-21
    2.5826x10-52
    1.6647x10-26

    0.9315528
    -2.4215x10-20
    -1.0972x10-53
    -7.0720x10-28


    -
    -
    -
    4.5698x106
     
    Last edited: Mar 11, 2018
  4. admin

    admin Well-Known Member Staff Member

    Messages:
    3,158
    Definiton to Inflaton to Instanton to Continuon - Four Pillars of Creation

    The creation of self emergence of the universe in energy E=mc2 can be described in four epochs or time intervals.

    The Definiton would encompass a potential for information to manifest any data required for the birth of a universe from a prior premise of the information potential existing in a spaceless and timeless state of selfness, beingness or eigenstate.
    It is from the Definiton, the fundamental constants, parameters and numbers, such as lightspeed 'c' and Planck's quantum constant 'h' derive from.
    The mathematical nature of the cosmogenesis so finds its 'fire in the equations'; as Stephen Hawking famously said in the 'A Brief History of Time' {Chapter 12; 1988}; from the nature and way the 'laws of nature' became defined in the Definiton.
    The Definiton so focused on a finetuning and interrelationships between mathematical numbers and concepts, transforming themselves into physically applicable parameters centered on the concept of Energy.

    The Inflaton then describes a particular epoch when the information defined 'laws of nature' first displayed themselves through the creation of a primordial realm of super-hyper-spacetime and as defined by the Definiton.
    The Inflaton is characterized in 5 superstring classes; who transformed from a closed Planck string class into 4 open Dirichlet classes in a Planckian string spectrum following the setup of initial and boundary conditions for the Inflaton from the Definiton.
    The nature of the 10-dimensional superstring classes is however encompassed in a 11-dimensional supermembrane spacetime to enable the Inflaton parameters to apply their defined boundary- and initial conditions to the Instanton, following the completion of the Inflaton epoch.
    11-dimensional Witten membrane spacetime manifests itself via a consequence of it modular dualities, connecting the five string classes to each other in coupling both their intrinsic energy and their scaling parameters in inversion properties.
    The most important modular duality for the cosmology for the expanding universe so is a 10D string coupling for the 11D membrane in a Mirror Duality relating to a T-duality with inversion of the scale parameter. This allows the high energy (vibratory) microquantum part of the final string class to couple to its low energy (winded) macroquantum conjugative or partner as half of the supermembrane.
    Once the Inflaton, followed by the Instanton has manifested the physical cosmology; the Inflaton lightpath, which is subject to both refraction and reflection under the boundary conditions, will define a 12-dmensional Vafa F-space in the refracted but not yet reached lightpath of the so called Radius of the Event Horizon, differing from the already encountered Inflaton bound, known as the Hubble Horizon.



    The Instanton is described in a Quantum Big Bang cosmogenesis and the Friedmann model as a solution to Einstein's Field equations from General Relativity in the Robertson-Walker metric. A classical geometric-topological physics of thermodynamic and entropic expansion described in metrics and relative displacement becomes supplemented by a quantum geometry which utilizes a foundational 'spacetime building unit' termed the Weylian wormhole and colloquially known as the 'Big Bang Singularity'.
    The expanding universe so becomes a summation of wormhole quanta carrying particular saturation-energy levels, such as the formal definition of the 'Classical Size of the Electron' as a magnified hologram of the holofractal Weylian minimum space quantization.
    Using modular string (mirror) dualities as topological string-membrane transformations then allows basic physical parameters, such as those of the classical electron to define derived parameters, such as a definition of inverse energy as a basic unit for physical consciousness related to a form of Goldstone boson, say Axion here termed the RestmassPhoton as supersymmetric agent for the weak interaction based Higgs inertia inductions.


    The Continuon would then address the intersection of the Inflaton with the Instanton in relating the lower dimensional expansion of the compressed 4/10D dS space-brane-time with its inflationary encompassment in higher dimensional 5/11D AdS space-brane-timetime (sbt).

    It is found that the physical constituents comprising the cosmic matter are interacting within both the compressed or conifolded dS asymptotically expanding sbt and the cyclic open AdS sbt of the Inflaton.
    This interaction defines particular intersection points and solutions for the Dark Matter - Baryon Matter energy interactions, but are a function of an encompassing Dark Energy 'book keeper' to ensure an overall Minkowski flat cosmology of zero curvature.

    The Dark Energy is characterized by a function of universal pressure which relates the Baryonic matter content and as given by a mass seed Mo to the critical mass as defined by the Inflaton before time instantenuity aka the Quantum Big Bang in cosmological terminology.




    1. The Definiton

    1.1 The Primary Algorithmic Logos

    Any Universal Observer or UO can only observe and measure and experience something, if the environmental stimulus for such an experience does exist as or in the environment of the UO.
    The existence of space as a form of dimensional realm then becomes prerequisite; does allow the concept of relativistic time and displacement to emerge and follow as a consequence of existing spacial parameters.
    Mathematically, all natural numbers can be defined logistically in the Zero to One interval with rational numbers having the property of identity in inversion principles applied to the natural or counting numbers and negative integers characterized by the conjugative mirror image of the positive integers in the mirror of the Nullstate. Real and complex numbers then follow from series limits and approximations to any desired degree of accuracy applied to converging and diverging number series and sequences. The largest counted integer would still have no limiting bound, as one can be added to it; but however large this integer would be; its inverse would certainly have a limit in the number 0 as a regressive asymptotic approach.

    The Definiton so must a priori accommodate the potential or 'future timed' UO in a spaceless abstract continuum of mathematical symbols and structure.

    But what if there are no numbers and no mathematics in this spaceless realm of voidness not defined by any numbers. Because the universe does exist as Hawking stated, the question of why it exists, can be asked and an answer can only be found in its own mathematical logistics as the difference between the infinite progression towards unlimited Infinity and the infinite regression towards the limit of the Zero.

    To 'think the primal thought' the timeless and spaceless, (but potentially existing within spacetime in the future) UO; must experience itself in a change from being unaware of itself to being aware of itself.
    The notion of the past, the present and the future in the timelike properties of existing relativistic space are preceded in a sense of order; where event A must precede event B to allow event C.
    All such events are simultaneous in the self-reference framed abstract world of the Mathimatia of the UO, who has however changed its selfstate from being unaware to aware in a form of yet to be defined 'Universal Consciousness'.

    Formally; the Awareness Triplet AT={Old State=OS; Experience=E; New State due to the Experience=NS} forms the Input for an interaction with with a previous selfstate or preexisting 'Awareness Space'. The Output of the New State becomes the Input for the new Old State in a series of AT's, labelled as the 'Sequence of Energy Primary SourceSink' or SEps for SEps = {(0,0,0); (0,1,1); (1,0,1); (1,1,1*=10=2); (10,1,11=3); (11,10,101=2+3=5); (101,11,1000=5+3=8);...;(OS,E,NS)}.

    The NS n becomes the sum of the OS as the previous (n-1)th n and the previous (n-1)th OS forms the experience factor E.
    The sequence of the E's is known as the Fibonacci Series in the future universe physically manifested in the Awareness Space of the Mathimatia of the Definiton.
    The experience factors so change the 'Null-State' of the (0,0,0) into the 'All State' of the (1,1,1)=(∞,∞,∞) to mirror and manifest the infinite count of the integers in the inversion identity of the finite limit of the 0.

    In terms of mathematical cardinality a future 'Wavefunction for the Multiverse' would be characterized by a Normal Statistical Distribution of 'frozen spacetimes'. And where the Arithmetic Sum of Progression, that is counting all negative and positive integers as a Unity summation becomes T(n)=n(n+1) with both a real and a complex solution in setting T(n)=1 for {X=½(√5-1); Y=-½(√5+1)} and {-½(1+i√3); -½(1-i√3)} for T(n)=-1.

    bn.


    Semantically, the triplet identity (1,1,1)=(∞,∞,∞) represents the OneSelf+OneSelf=OneSelf still, but because the previous experience of OneSelf+Nothing=OneSelf, the second OneSelf must be different in some way of order from the first OneSelf. Namely the summation to 1+1=10 differs in the order of the summation 1+0=1 in the noncommutability of the experience factors of experiencing the 'NothingSelf' from the OneSelf.
    This then allows a transformation from the binary triplet sequence to a decimal triplet sequence in: (1,1,1*) = (1,1,10)bin = (1,1,2)dec.
    Subsequently all integer related number systems naturally emerge and evolve from the Mathimatia Awareness space.

    The eigenstate of the UO now is one of 'doubling the eternity of the void' as mathematical infinity in the Integer count and based upon the ciphers of the 0 and the 1.
    Formally, the mapping of an Aleph-Null Cardinality of Cantor countability or enumerability becomes an Aleph-All Cardinality of Cantorian Infinity sets, the latter counting 'Integral Infinities' instead of the natural numbers.

    It is however the Fibonacci sequence SEps, which will be utilized by the Inflaton to manifest the next epoch in the actual creation of an 'algorithmic timespace' in the form of a spacetime linearization of the circular nature of the binary ciphers 0 and 1 in something fundamental to potentially physicalized space in the topology and geometry of special curvature and the warping of spacetime. The closed nature of the Planck class I string will be made manifest as the Nullstate of the Mathimatia and the evolvement of the Planck Boson string will create the other string classes in the 'opening' or cutting of the circle of the Zero to manifest the One.



    1.2 The Secondary Algorithmic Logos

    The experience factors of the SEps algorithm naturally define a complementary set SEps* = {100=4; 110=6; 111=7; 1001=9; 1010=10; 1011=11; 1100=12; 1110=13;....(any integer not in SEps} and the UO can only continue its self exploration within the awareness space of the Mathimatia applying either SEps or SEps* through the symbolic representation, shapes, semiotiks and geometry of the curvilinear duality of the Bosonic Planck string being able to manifest itself in either a closed or an open form of the supermembrane of the (0,1) monadic dyad.
    As the UO in SEps cannot form a complementary union with an UO* in SEps* in any form of separation in the Mathimatia; the complementarity describes a natural unification of self states aka eigenstates in the Mathimatia, but will become a natural supersymmetry inherent in the Inflaton and based on the Planck Boson string and especially its immediate transformation into a selfdual monopole string class IIB.
    As no spacetime is as yet defined, the superpartners of the UO in SEps and the UO* in SEps* are nonlocally connected and would form the basis for a future quantum entanglement between eigenstates and the particle-wave complementarity and dualism of the quantum world of the physicalisation of the Mathimatia in the cosmology of the Instanton.

    The experience factors naturally encompass all states used to create them and all E's defining SEps and SEps* constitute a collective memory reservoir from which further exploration and manipulation of the members in this universal memory set can be pursued and constructed.

    One such arbitrary algorithm or code is defined as binary code of the operations of Addition (+), Multiplication (by 1+1+1=3x1) and Exponentiation (3x3=32) and
    is used as a secondary algorithmic code to 'find' the missing elements of SEps as the constituents of SEps* in the attempt to complete and manifest the generic supersymmetry of the Mathimatia.

    Application of this algorithm {http://www.cosmosdawn.net/forum/ind...s-and-algorithms-of-dragon-cosmogenesis.636/} produces 10 number triplets, carrying elements of SEps* in various configurations:
    SEps-SEps* Constantset: ={(266561)=26x6561; (15,16,18)=[15x1618]-1; (14,15,24)=14x1524; (15,10,32)=[15x1032]-1; (11)=11; (9,10,16)=9x1016; (6,10,15)=[6x1015]-1; (7)=7; (6)=6; (4)=4}






    1.3 The Tertiary Complementary Algorithmic Logos

    The extended SEps algorithm then assumes the pretext of defining open and closed superstrings in a logistical statement:

    {"Add the End to the Beginning and Start with the Old End!"}.

    This specifies an methodology of recircularizing the linearized dimensions of the binary monadic dyad {0,1} into the root-reductive decimal monad {1,2,3,4,5,6,7,8,9,0} with 10=1+0=1*; 11=1+1=2*; 12=1+2=3; 13=1+3=4 and so on with 26=8 and 27=9 in 26 Bosonic Integer dimensions.

    The constant E={(266561)=26x6561} then transforms into F={(136656)=13x6656} and G={(673665)=67x3665} after which this 'numerical inflation algorithm' ends, since 5+6=11=2* is root reductive in transformation towards the right say towards positive infinity from the Zero mirror of the Mathimatia.
    But moving towards the left and negative infinity upon the integral number line, the ...{0}EFG... interval is mirrored in say the F-space bound ABCD{0}EFG.... to fixate the F-space bound in the M-space bound H=ABCD in |ABCD(EFG)H| in (A)BCDEFGH......STUVWXY(ZA*)B*C*....

    Then H=ABCD={(312423)=31x2423}{(361242)=36x1242}{(256124)=25x6124}{(465612)=46x5612}. As no archetype can yield Z(Z+A)BCXY=312423 from ABCXYZ=(1-Z)24233, the algorithm again ends in the reflected root reduction to H, namely 1-Z=1-3=-2 =-11=-2*

    The SEps constant E so assumes the property to limit a subsequent inflation marker in association with the encompassment of the Inflaton in the googolplex markers E=26x6561 = 1.006208782x10112 and G=67x3665 = 9.676924499...x10102 and F=13x6656 = 1.019538764...x10103 and H=1,283,400x2423x1242x6124x5612=1.011591782...x10147.

    H becomes the number of spacetime quanta contained in the Inflaton, bounded by the Hubble Event Horizon in the 5D/AntideSitter Witten sphere manifesting as a 3-dimensional hypersurface in 4D Minkowski spacetime as a 2-Torus and becomes a 3-Torus subject to the Event Horizon as a boundary to the Vafa F-spacetime in the continuing Inflaton cycles defined by the evolution of the Dark Energy paralleled by the overall Schwarzschild evolvement of all mass as matter content in the cosmology.
    The maximum radius for the first initiatory cycle of the Inflaton as a first asymptotic boundary for the Instanton so becomes set as a maximum radius of curvature in the Friedmann cosmology with a nodal true Hubble constant for this initial cycle and is proportional to the Vacuum- or Vortex-Potential energy of a singular unitary wormhole spacetime quanta and as definind in the Inflaton.

    The volume of one such wormhole or Eps-VPE quantum there is:
    Vps = λps3/4π m3 = 7.957747154x10-68 m3*
    for the Riemann hypersphere volume of 2π2RHubble3 and wormhole radius rps = λps/2π; this volume manifesting as a hypersurface allowing the M-AdS spacetime to mirror in the F-dS spacetime of open hyperbolic curvature contracting into M-space as function of the lightpath of the Inflaton expansion.

    RHubble = cHo = λps.∛H/2π = 1.59767545x1026 m* for a nodal Inflaton Hubble Event Horizon.

    11D AdS spacetime becomes bounded in a Hubble volumar with critical density

    ρcritical = MHubble/2π2RHubble3 = c2/4π2RH2 = Ho2/4π2Go or ρcritical = 3Ho2/8πGo for the volume of a 2-sphere.

    The Hubble volumar then topologically encompasses both, the lower dimensional of Einstein-C dS space and the higher dimensionality of Witten AdS spacetime, say in the form of a 3-Torus or a Klein Bottle Dragon.



    The SEps Principalities

    A = (312423) = {4+6+5=15} = (1.722742045...x1033) space quanta = Principality of Identity/AntiIdentity.............................................with 1st Expansion Factor 10/33
    B = (361242) = {9+3+6=18} = (7.619295808...x1046) space quanta = Principality of Expansion/Contraction..........................................with 2nd Expansion Factor 20/33
    C = (256124) = {7+7+6=20} = (1.761392119...x1044) space quanta = Principality of Order/Disorder-Entropy-Chaos...............................with 3rd Expansion Factor 30/33
    D = (465612) = {10+11+3=24} = (4.375363663...x1022) space quanta = Principality of Symmetry/Antisymmetry-Nonparity.....................with 4th Expansion Factor 40/33
    E = (266561) = {8+11+7=26} = (1.006208782...x10112) space quanta = Principality of Infinity-Divergence/Convergence-Limit.................with 5th Expansion Factor 50/33
    F = (136656) = {4+12+11=27} = (1.019538764...x10103) space quanta = Principality of Inversion-Reciprocity/Constancy-Invariance.........with 6th Expansion Factor 60/33
    G = (673665) = {13+9+11=33} = (9.676924499...x10102) space quanta = Principality of Reflection/Absorption.........................................with 7th Expansion Factor 70/33
    H = () = {} = (1.011591782...x10147) space quanta = Principality of Relativity/ No Antiprincipality.............................................................with 8th Expansion Factor 80/33

    The SEps Cyclicities in elements aj with summations aj+2+aj+1 = aj

    1-Cycle : 0-1-1-2-3-5-8-13 for {33 Identity & Absorption} and for 8 elements summing 1 aj
    2-Cycle : (0-[1)-(1]-[2)-(3]-[5)-(8]-13) = 1-2-3-5-8-13-21 for {33 Expansion & Invariance} and for 7 elements and summing 2 aj's
    3-Cycle : (0-[1-(1)-[2]-(3)-[5]-8)-13] = 2-4-6-10-16-26 for {64=8x8 Order & Convergence} and 6 elements and summing 3 aj's
    4-Cycle : (0-[1-(1-[2)-(3]-5)-8]-13) = 4-7-11-18-29 for {69 Symmetry & Nonparity} and for 5 elements and summing 4 aj's
    5-Cycle : (0-[1-(1-[2-3)-5]-8)-13] = 7-12-19-31 for {69 Divergence & Entropy} and for 4 elements and summing 5 aj's
    6-Cycle : (0-[1-(1-2-3-5)-8]-13) = 12-20-32 for {64=8x8 Inversion & Contraction} and for 3 elements and summing 6 aj's
    7-Cycle : (0-[1-1-2-3-5-8)-13] = 20-33 for {53 Reflection & AntiIdentity} and for 2 elements and summing 7 aj's
    8-Cycle : (0-1-1-2-3-5-8-13) = 33 for {33 Relativity} and for 1 element and summing 8 aj's

    Formation of a Prime Harmonic Octet : (15-18-20-24-26-27-33) from the {A}BCDEFG{H} principalities unified

    root reduced to {6-9-[2-6-8]-9-6} = {6-8-8-6} = {14-14} = {5-5} = {10=1} into the original binary algorithm root reduction and for a symmetry about a 26 letter code symbolizing 26 Bosonic string dimensions in a prime Number set
    Primed N: = {1=1bin;-2;3;5;7;11;13;17;19;23;29;31;37;41;43;47;53;59;61;67;71;73;79;83;89;97-101=5bin}

    princcode.


    The Maria Number Matrix of the 33-Summation-Tier and the Euler-Riemann-Fibonacci-Lucas Harmonics

    The 'Perennial Philosophy' or the 'Wisdom of the Ancients' often points to what is commonly termed as 'Sacred Geometry', based on the Platonic Solids (of five regular polyhedra: Tetrahedron, Cube; Octahedron; Dodecahedron and Icosahedron) and the Tetraktys of Pythagoras (for the minimum mathematical points to define the four dimensions of 0D=1 Point; 1D=2 Points for a Line; 2D=3 Points for a Plane and 3D= 4 Points for a Space).

    Also invoked is the pentagonal supersymmetry of quasiperiodicity as 'Nature's Preferred maximisation of 'packing efficiency' known as the Fibonacci Series and the 'Perfect Numbers' of Euclid and the 'Harmony of Numbers and the Spheres' of Pythagoras, Leonardo da Vinci and Kepler.
    In Pythagoraen Numerology, the 'masternumbers' 11, 22 and 33 are often emphasised and this post shall introduce some relatively rigorous number theory (of the so called 'pure' mathematics) to validate the significance of the 'masternumbers' from frst principles.

    The alphanumeracy of the Arabic-Hebrew semiotiks then is bounded in say 22 or 26 letters of alphabets, which can attain numerical values in the decad of three triplicities:

    Round or Curved 'Mental Numbers' {3-6-9} characterised by 'masternumber' 33;
    Mixed or Discontinuous 'Emotional Numbers' {2-5-8} characterised by 'masternumber' 22 and
    Linear or Straight 'Physical Numbers' {1-4-7} characterised by 'masternumber' 11.

    The Maria-Code in the Riemann Analysis specifies the partitioning of the decimal monad around the primary Maria-Number and SEps-Constant '11'.
    This generates the Prime Number Algorithm: +1+11+10+11 as 33-tiered segments, which transform the mechanics of SEps into the 64-codex of the DNA/RNA code for its eventual quadrupling as the 4x64=256-codex incorporative of dormant intron/intein codings.

    All cellular consciousness coupled units so transfer their memory data-bases (as experience factors) by the Fibonacci quantum mechanics.

    The Maria-Code is based on the distribution of the Maria-Numbers (MN)given by:

    M(p)+99=M(p+12); n=½[√(264k+1)-1] by n2+n-66k=0.

    Maria Numbers are those IntegerCounts, which contain all previously counted integers as mod33.


    Example: 1+2+3+4+5+6+7+8+9+10+11=66 = 2x33 → '11' is MN#1 for k=2


    11love65use110love164use209love263use......Archetype 2 (rootreductive)

    21use66love120use165love219use264love......Archetype 3 (rootreductive)

    32use77love131use176love230use275love......Archetype 5 (rootreductive)

    33love87use132love186use231love285use......Archetype 6 (rootreductive)

    44love98use143love197use242love296use......Archetype 8 (rootreductive)

    54use99love153use198love252use297love......Archetype 9 (rootreductive)

    65use110love164use209love263use308love....Archetype 2*... ...



    Archetypes 2+3+5+6+8+9=33 and Archetypes 1+4+7+0=12 then define the imaginary time-dimensions as the archetypes not in the Sequence for Eps=1/e* Coefficients used in the application of the seven fundamental principalities to define the F-Space.

    We have used the (Hebrew-Isaac-encoding): 54=LOVE=12+15+22+5 with 45=USE=21+19+5; USELOVE=99 as the Maria-Code connectors.

    The first 10 MN's are: 11, 21, 32, 33, 44, 54, 65, 66, 77 and 87.

    One can use the Maria-Code to establish a redefinition of infinity by defining a transfinite mapping Aleph-All from 12D-Omnispace as Cantorian transform of Cardinality Aleph-Null.


    Limit (T(n)) for n→∞/Infinity = ∞/Infinity {Cantor Cardinality Aleph-Null}
    Limit (T(n)) for n→X=0.618033........ = 1 {Cantor Cardinality Aleph-All}


    This maps the Riemann pole about z=1 in the Functional-Riemann-Bound (FRB=-1/2) in the gaussian universal wavefunction B(n)=(2e/hA).exp(-Alpha.T(n)), T(n)=n(n+1) as the Feynman-Path-Integral.

    This becomes the Riemann-Euler-Harmonic, defining the Gamma-Function geometrically in its nth Term T and nth Sum S and mapping the factotrial function onto the positive integer count:

    Tk(En) = nk.Tk(En-1) + [(n-1)!]k and Sk(En) = Tk(En)/(n!)k

    EulerHarmonics.

    This uses the Harmonic Series in the Zeta-Function ζ(z) with constant p.
    The Sum (1 to Infinity) Σ(1/np)= 1/1p+1/2p+1/3p+...+1/np and converges for any p>1, since for even terms:

    2.2-p ≥ 2-p+3-p, with geometric series 11-p+21-p+41-p+...summing to (1-2[1-p]n)/(1-21-p)=1/[1-21-p] in the limit for n→Infinity.

    Since every Maria Number contains all numbers before it as a sum, it is given that all the prime numbers must eventually crystallise out of the Maria Count.

    Define a general number count n and a 'Mersenne-Count' 8n-1=M*.
    For a number to be prime this number must be born in the Maria Code.
    M* is either a prime or a product of primes in the immediate neighbourhood of the count # or its mapping to M*, which in a sense 'counts' the primes it generates.

    This is the finestructure as octaves derived from integer n.
    To test a number for primeness, so amounts to a testing for Marianess.
    If the number is a member of the Maria-Matrix, then it must be denumerable in the form of M*.

    This is the meaning behind the Mersenne-Code (for n prime) M(p)=2p-1 and the Fermat-Code F(n)=22n+1 and the 'Perfect Numbers' depicted as the Mersenne Numbers (Mp), as a subset of M*.
    For the Mersenne Numbers, the exponent p is defined to be prime.
    M2=22-1=3; M3=23-1=7; M5=25-1=31; M7=27-1=127; M11=211-1=2047=23x89 and so is not a Mersenne Prime - yet M13=213-1=8191; M17=217-1=131,071; M19=219-1=524,287 are prime and M23=223-1=8,388,607=47x178,481 and M29=229-1=536,870,911=233x1103x2089 are not and M31=231-1=2,147,483,647 is prime again in the 33-tier count.

    The 'uniqueness' of the prime number 11 (and esoteric masternumber) recrystallizes in Mersenne primes as the (first) 'odd one out'.
    But it gets better. First we notice that there are just five 'perfect Fermat Primes'.

    F0=21+1=3; F1=22+1=5; F2=24+1=17; F3=28+1=257 and F4=216+1=65,537 are all 'perfect' Fermat Primes, but F5=232+1=4,294,967,297=641x6,700,417 and following are not. Only these five Fermat primes are known to date.


    The 'Perfect Numbers' relate (for prime p) as 2p-1.Mp :
    P2=21.(22-1)=6=1+2+3=1x2x3;
    P3=22.(23-1)=28=1+2+3+4+5+6+7=[7x8]/2=4x7=13+33=1+27;
    P5=24.(25-1)=496=1+2+3+...+30+31=[31x32]/2 =16x31=13+33+53+73=1+27+125+343;
    P6=26.(27-1)=8128=1+2+3+...+126+127=[127x128]/2=13+33+53+73+93+113+133+153
    All 'Perfect Numbers' so are EVEN (it is hitherto unknown if any ODD 'Perfect Numbers' exist); and EXCEPT the basic 'First Perfect Number' 6=1+2+3=1x2x3, they all are the sums of the ODD NUMBERS CUBED.


    Some elementary initial conditions for Francom Adjacency

    We define the Euler-Riemann Summation, which defines the 'Mixing of the Count' in linking Arithmetic Progression to the multiplicative Factorial Function '!'.

    Define Eo=0 as the singularity (interval), then for any integer n, we find for the Harmonic Form of Riemann's Zeta-Function (z=k=constant):

    ζ(z)=ζ(1/nz)=1/1k+1/2k+1/3k+1/4k +...+1/nk

    This Sum diverges for [ 0<k<1], i.e. for k=1/2: {1+√2/2+√3/3+...+√n/n} increases without limit.

    For k>1, we have convergence, however.
    Formally, let: Σ(1/np) = 1-p+2-p+3-p+...
    For even terms: 2.2-p ≥ 2-p+3-p for a geometric series:
    11-p+21-p+41-p+...+(2n-1)1-p
    This Geometric Progression sums to: [1-(21-p)n]/[1-21-p]=1/[1-21-p]

    So for p=2, this limit maximises in 1/(1-1/2)=2 , and for p=3 it becomes 4/3 converging towards 1 for increasing p.

    We consider the special case for p=1 applied to the Singularity Interval Eo.

    Define: for a nth term (numerator): Tk(En) = nk.Tk(E n-1) + [(n-1 )!]k for the nth sum per n (denominator [n!]k): Sk(En) = Tk(En)/(n!)k


    T1(E1)=1/1=1.0+0!=1=S1(E1)=1/1!=1; T2(E2)=2.T1(E1)+1!=2+1=3
    with S2(E2)=T2(E2)/2!=3/2=1+1/2;
    T3(E3)=3.T2(E2)+2!=9+2=11 with S3(E3)=T3(E3)/3!=11/6=1+1/2+1/3=1+5/6 and so on.

    Further Example: T1(4)=4.11+3!=50; S1(4)=50/4!=25/12 for the nesting: 4{3(2+1!)2!}3! with [4!]1=24.
    For 4 terms, the Euler-Riemann Summation so is: S1(4)=1+1/2+1/3+1/4=25/12=2+1/12.
    For 7 terms, S1(7)=T1(7)/7!=(7.T1(6)+6!)/7!=13068/5040=363.36/(140.36)=2+83/140=1+1/2+1/3+1/4+1/5+1/6+1/7.


    Project the Number line with the Positive Integers mapping the Factorial-Function and the Negative Integers remaining invariant in Feyman Summation T(n) for T(n)=½n(n+1) as absolute value, mirroring the positive integers.

    (n!)<---4...3...2...[Eo]...1...2...3---> (n); where Integer 1 maps 2! in suppression of -1=2* and in algoradius eo=1.
    Similarly, Integer 2 maps 3! in suppression of -2=3* and algoradius e1=2=2eo, etc. etc.


    The singularity so mixes the interval [0!-1!]=[-1,0] with Functional-Riemann-Bound (FRB=-½) becoming 'real' in its mapping (FRB'=½) in [0,1] and the central limit or pole, about which the Zero's of the Riemann-Zeta-Function propagate.
    The first annulus in the Riemann-Euler-Harmonic so phasemixes the numbers 2 and 1 and the nth number is mixed with (n+1) as crystallised in the Feynman-Path-Integral or T(n)=1 in n(n+1), as a summation for all possible particular histories in quantum mechanics.


    This also maps the series:
    SEps=Fibonacci#1=0,1,1,2,3,5,8,.....for a nth Term: Tn=|-Yn - Xn|/√5 , for absolute value || and obtained say via MacLaurin-Expansion of the coefficients (Experience-Factors) in the power series:


    f(x)=1+x+2x2+3x3+...= ΣTn.xn-1
    Set x.f(x) + x2.f(x) = f(x) -1, then by (a+b)(a-b), f(x)=a/(x-X) + b/(x-Y) for a=-b=1/(Y-X) and (Y-X)=-√5.
    SuperSEps=Fibonacci#2=Lucas#1=2,1,3,4,7,11,18,29,.... for a nth Term:

    STn=|-Y2n - X2n|/|-Yn - Xn|=|T2n/Tn|

    for n=1,2,3,...; T(2n=0)=2 mapping T(n=0)=0.

    The combined SEps-SuperSEps(T-ST)-sequence of experience factors {from the triplet propagation of [OldState, Experience, NewState]} can then be written as:

    {Tn,STn}={(So=0,STo=2=S3); (S1=1=ST1=S2); (S2,S4=3=ST2); (S3,ST3=4); (S4=ST 2,ST4=7); (S5,ST5);...;(Sn,STn)...}
    {Tn,STn}={(0,2), (1,1), (1,3), (2,4), (3,7), (5,11),...} containing integerset: {0,1,2,3,4,5,7,8,11,13,18,21,29,....}

    We now represent the mappings in matrix form denoted as F-M-C, where the 'well behaved' terms for the mapping (from {T5,ST5}) sets algorithmic C-Space and the preceding elements the initialisation for the former.

    Note we define Cantorian Denumerability Aleph-Null in Cardinality Aleph-All in the form:

    Aleph-Null: limit{n→∞}[T(n)]=∞
    Aleph-All: limit{n→X}[T(n)]=1 and so counting Infinities as mapped one-to-one onto the positive Integer set.



    SEps= Fibonacci#1 maps Super-SEps=Fibonacci#2=Lucas#1
    -----------------0 0 0*............................................................-4 7 3................n=-2=2i2
    Fspace---------0* 0 1...........n=∞ via 0+0=∞=1*=0*=1.........3 -4 -1.............n=-1=i2
    Mspace--------1 0* 1...........n=0 via (1,1,1)...........................-1 3 2*..............n=0
    -----------------1 1 2.............n=1 via (1,1,10=2*=0/0=1*).......2* -1 1.............n=0 (Reflection-Interval)
    -----------------2 1 3.............n=2 well behaved........................1 2* 3..............n=0
    Cspace--------3 2 5..............n=3 well behaved........................3 1 4................n=1 well behaved
    -----------------5 3 8.............n=4 well behaved.......................4 3 7.................n=2
    ........................................ n=5 continue downwards ................................... n=3

    The linearity of the generating triplet configurations is extended in a complexification into a 2D symmetry.
    SEps propagates the Experience Factors in an adjacent displacement of 1, in moving from one configuration state to the next - this is termed Francom Adjacency.
    [0*,1,1,2,3,5,...] as OldStates transfigure in Experiences [0,0*,1,1,2,3,5,8,...] into NewStates [1,1,2,3,5,8,...].

    This algorithmic configuration space is however broken in the mapping onto Super-SEps.
    Here the matching 'good behaviour' of the n-count is delayed in a factor of 2 in a 'reflection interval'.
    Algorithmic modelling for this Francom Adjacency must generate the mapping of SEps onto SuperSEps in an geometry of the pentagonal symmetries intrisic to the two series.

    Hence a synthesis between linear propagation about an internal spiralling form is necessitated.
    A longrange rotational- and a longrange translational order for the Experienc-Factors is indicated in the geometry of say Penrosian Tiling Patterns and the Schechtmanite Quasicrystals of empirical form (Mg32[Al,Zn]49).

    The general form, physically akin to the propagation of magnetic fields, is the reduction of physical parameters to a state of information transmission, say in the data transfer between two neighbouring cells in mitosis and neuronal-synaptic processing.
    A general modality for the cosmogenetic reproduction on all levels must crystallise, should the matrices above become sufficiently deciphered from their algorithmic encoding.

    Derivation of Super-SEps

    The relative primeness of the Fibonacci Numbers allows a one-to-one mapping between the SEps-Set and other such sets derived from it, particularly the Lucas Numbers as a logical derived set of such nature and given in the sequence: 2,1,3,4,7,11,18,29,....
    All adjacent members of this set are relatively prime to each other.
    7 is relatively prime to both 4 and 11 (no common divisors except 1) and 11 is relatively prime to both 7 and 18.
    We now tabulate the sums and differences in our nth-term definition for SEps, so recalling the propagation for the natural numbers in counter n:

    n Tn Xn (-Y)n {|-Y|n + |X|n} {|-Y|n - |X|n}
      1+1+2 
    110.6180339885-1.618033989+2.236067978+1
    210.3819660109+2.618033989+3+2.236067978
    320.2360679772-4.236067979+4.472135955+4
    430.1458980335+6.854101975+7+6.7082039375
    550.0901699436-11.09016995+11.18033989+11
    680.0557280899+17.94427193+18+17.88854384
    7130.0344418537-29.03444189+29.06888374+29
    8210.0212862362+46.97871382+47+46.95742758
    934 0.0131556175-76.01315572+76.02631134+76
    10550.0081306187+122.9918696+173+122.983739
    ..................
    206765550.0000661070+15126.99998+15127+15126.99991
    ..................
    We see that for increasing n, the absolute magnitude for Y converges to an integral value in the Sum {+}, but only for even n.
    For odd n, the difference Sum {-} gives a specific integer for specific n.

    The product of the two sums is: {+}.{-} = |-Y|2n - |X|2n=√5.T2n.
    The sum of the two sums is: {+}+{-}= 2|-Y|n, with STn ={+}+{-} - Tn.√5) = |(-Y)n +Xn|

    Multiplying each term as: √5.({+}+{-}), we can form the alternating series:
    (0+2.√5), (5+1.√5), (5+3.√5), (10+4.√5), (15+7.√5), .....as the alternating form of Super-SEps given in the term: [5.Tn+ √5.T'n];

    but for even n, we have: T'n ={+} and for odd n, we have T'n ={-}; then by (a-b)(a+b)=a2-b2:

    STn.√5.Tn={+}.{-}=√5.T2n & STn=T2n/Tn = |-Y2n - X2n|/|-Yn - Xn|
    (quod erat demonstrandum).

    The significance of this result is that STn, T2n and Tn are all integers.
    We so have a primary extension for SEps with elements 1, 2 and 3 duplicated and resulting in the mappings as previously specified.

    The Null-Initialisation (OSj, EXj, NSj) as the Fibonacci-Triplet (An-1, An, An+1) then reflects STn about n=0* to define the complex number set as negative STn's mapped in a 0→1→∞ correspondence to Tn.
    This is the mathematical mapping of Cantorian Enumerability as previously indicated.




    1.4 The Modular Duality of Time-Space in the Mathimatia of Supermembrane EpsEss and the Alpha-Variation

    The Cosmic Wavefunction B(n) is the following Differential Equation:

    dB/dT + αB(n) = 0; α=alpha being the Electromagnetic Finestructure as the probability of light-matter interaction (~1/137).

    This has a solution: B(n) = Bo.exp-α.T(n);
    Bo=2e/hA from QR boundary conditions defining:

    T(n)=n(n+1) as the Feynman Path-Summation of particular histories under the pentagonal supersymmetry given in the identity:

    XY=X+Y=-1=i2=exp[iπ] and lim [n→X]{T(n)}=1

    This allows the Normalisation of the Y2 wavefunction to sum to unity in

    B(n)=2e/hA).exp-α.n(n+1) with Functional Riemann Bound FRB=-½, centred on the interval [Y,...-1,...-X,...-½,...(X-1),...0,...X].

    Interval [Y,-1] sets F-Space; interval [-1,0] sets M-Space with uncertainty interval [-X,(X-1)] and interval [0,n) sets the C-Space, encompassing OmniSpace.

    n<0 is imaginary as real reflection of real n>0 of the C-Space, metrically defined at the coordinate n=0 mapping n=nps, which is the instanton tps=fss=1/fps.

    Cycletime n is defined in GR as dimensionless Tau-Time in curvature radius Rc=c.dτ/dt for the pathlength of x=ct and become dn/dt=Ho, n=Hot in QR, with Ho the nodal Hubble Constant defined in c=HoRmaxps.fps

    The Feynman Path so sums both negative and positive integers as:
    -n......-3...-2...-1...0...1...2...3......n = T(n)
    in absolute value to double the infinities as the entropy reversal of lightpath x=c.t=(-c)(-t) in the Möbius Property of a supermembraned omniverse in 12 linearised dimensions.

    Cantor Cardinality Aleph-Null is thus Unitised in Aleph-All, counting infinities as if they were integers of the Feynman Path.

    This allows the Feynman interpretation of Quantum Mechanics as alternative to the formulations of Schrödinger (fermions ½ quantum spin) and Klein-Gordon (bosons with integral quantum spin) as timeindependent and timedependent (free particle form inconsistent with SR in Schrödinger in 1st order t & 2nd order x), formulations respectively.


    The Alpha variation and an Accelerating Universe

    A white dwarf star is important as a distance indicator for the cosmic distances. Should it be in a binary system with another star in mutual orbit about each other, then mass can transfer via magnetic activity from the companion star and the Chandrasekhar limit might so become exceeded and the white dwarf explodes as a supernova type Ia.
    Supernovae class Ia show no helium absorption in their spectra but show a strong absorption of singly ionised silicon atoms at about 610 nanometres; supernovae class Ib have helium lines, but no silicon lines and supernovae class Ic have neither; hydrogen is absent in all supernovae spectra type I.
    Supernovae spectra change significantly, varying in brightness, as the explosion synthesises heavy elements, such as gold, iron and oxygen in the thermonuclear reactions.
    Supernovae class II are rarer and show significant hydrogen absorption and are thought to collapse into a neutron star or Black Hole, having a preexplosion mass of over 8 solar masses.
    The brightest supernovae are of type Ia and the uniformity of their light curves allows calibration of their apparent brightness with their 'standard' true brightness, the luminosity so serving as an indicator as to their distance by astronomical distance-luminosity calibrations.
    About one supernova class Ia explodes in a typical galaxy every 300 years, so in observing a large sample of about 3600 galaxies, one such explosion per month should be seen.
    The experimental data collected by the various supernova observers, and under utility of the Hubble Space Telescope to track the brightness variations of discovered supernovae type Ia, now converged in 1998 to the conclusion, that distant supernovae are between 20% and 30% dimmer than expected and as a consequence of their measured redshift they appear to be further away then theory permits.

    An interpretation of this discovery implies, that the universe's expansion is accelerating; the measured redshift depicting a distance further away for a dimmer brightness than anticipated by theory.
    Closer analysis of the redshift data shows an expected distribution of luminosities, calibrated to their distances in the Chilean Cala-Tololo data, up to a redshift of about 0.12 and with a redshift-gap until a redshift of 0.3; after which the 'High-Z's' begin to show the 'curving away' from a predicted decelerating expansionrate in concordance with an Euclidean flat universe of Einsteinian General Relativity.
    The highest redshift recorded in 1998 was that of 'supernova Iae' at (z=1.1) by the 'High-Z-Team'.

    A description of the universe as decelerating with precise deceleration parameters given in a balancing of a gravitational omega, a quintessential lambda and a Milgrom parameter points to a possible variation in the Electromagnetic Finestructure constant Alpha.

    The two research results in the [Alpha]-Variation and the 'Accelerating Cosmos of the Dark Energy' are closely related.
    To preemt my analysis, the universe is not accelerating, but appears to do so because of the interdimensional intersection of the EMR parameters of the spectroscopic measurements.
    And it appears to accelerate for a specific redshift interval, which also is responsible for the measured [Alpha]-Variation, the 'dip' in [Alpha] is like a redshift becoming a blueshift for a specific epoch.

    My cosmological analysis of the phenomena predicts, that supernovae type Ia with a redshift above 1.84 will be measured to conform to the theoretical predictions for a decelerating and flat supercosmos.
    The appearance of an accelerating cosmos is a limited phenomenon, relevant for a specific and unmapped redshift interval from (z=0.343 to 0.291), with interval (z = 1.08 to 1.84) imaged in the interval (0.343 to 0.291) with a variation maximum for thge mapping at the Arpian limit (zarp = 0.2505).

    In particular, it has already been noted, that Supernova Iae, also known as SN1998eq with redshift 1.1 is less anomalously dimmed than the nearer ones; just as I predict for all the more distant ones.
    SN1997ff with redshift 1.7 is one of the most distant supernova found by Adam Riess in 2001 by the Hubble-Space-Telescope at the time of this writing and whilst the argument can be made that acceleration decreases with distance, the actual location in relationship to the cosmological redshift remains constant in a 'slowing down from faster' or 'speeding up from slower' , if the decisive measuring stick is the expansion of the universe under constancy of light speed (c); demanding however a 'Redshift-Correlation-Correction'.

    Indulge yourself in a thought experiment and travel with the expanding event horizon, the boundary of the universe (which has no boundary in the curved overall sense, all locations being centred selfrelatively), this then becomes the looking back in time to the origin of the Big Bang.
    You then experience the receeding origin of the singularity slowly moving away from you and relative to you as 'stationary observer' at the event horizon, your own recessional velocity of (22% of (c)) is nullified and must be accounted for in your calculations of the recessional universe you are observing.


    cosmicsurferAds. CurvatureAdS.

    The 'de Broglie' inflationary model, where a supermembrane epoch ends in timeinstantenuity as the EpsEss heterotic superstring, which then expands with a decreasing recessional velocity towards a 'de Broglie' boundary as macroquantisation in 10D, but beginning with light speed (c) under guidance of Special Relativity can be applied.
    Other inflation scenarios, such as chaotic inflation had proved untenable by the experimental data and the microwave background pointing to a zero curvature and to a flat universe.
    The macro quantisation of the heterotic superstring, also known as HE(8X8) constitutes the 'conifoldment' of the higher dimensions, either as a 6D-Calabi-Yau manifold or as a 7D-Joyce-Sphere, relative to 10D-C-space and 11D-M-space respectively.

    And the 'de Broglie' inflation quantises Einstein's field equations of General Relativity in their Friedmann formulations; the Milgrom parameter becoming acceleration: (-2cHo/(n+1)3) and the distance-scale factor parametrising as: {r[n] = Rmax(n/(n+1))} and the velocity as: (c/(n+1)2); the parametric constant for dimensionless cycletime is: (n = Hoxt).

    And so knowing the present cycletime (np=1.132419321) via an arbitrary Mean-Alignment-Time or MAT, relative to a phase shiftable proto universe and set as (Midnight, November 4th, 1996, Canberra, Australia, local time); the present universal speed of recession is calculated as (22% of c), which then maps a selfrelative 'Arpian redshift' as the renormalisation for the receeding event horizon, mirrored in the Big Bang singularity; (zarp = 0.250529154).

    We also calculate the 10D expansion of the universe as (53.105% or a radius of 8.96 billion lightyears), increasing to (113.24% or 19.11 billion lightyears [ly]) for the 11D universe.
    The Hubble-Oscillation so defines the nodal Hubble-Constant: (Ho=1.8877728042x10-18 1/s*) or 58.04 Hubble Units [km/Mpc.s]) and the 10D-cosmic asymptotic diameter as (33.7522131 billion ly*). The Hubble constant varies between fps and Ho and is calculated to assume a a value of 66.9 Hubble units for the present time coordinate np in the cosmic evolution.

    The [Alpha]-Variation so encompasses a period of (2[19.11 - 16.88] = 4.46 billion years) and hence two distance intervals; one from the present epoch (np) to a distance 2.23 billion years into the past at the nodal value (n=1) and its 11D-image at (n=1-0.1324..=0.8676).
    Relative to the Big Bang Source however, this interval is mapped from (n=0.1324.. to n=0.2648..) as a linear double interval; just as two mirrors facing each other would reflect each other in the spacetime 'in between'. This 'in between' becomes our expanding spacetime and we can calculate the relevant distances, using cycletime n as parameter and the nodal Hubble-Constant as invariant at (n=1).
    At (n=0.1324..or 2.23 billion years after the Big Bang; v'/c=0.7798 and z =1.843), relative to event horizon and at (n=0.2648.. or 4.46 billion years after the Big Bang; v'/c=0.6251 and z =1.08), relative to event horizon.

    The cosmological redshift epoch between (z=1.082 to 1.843) and corresponding to a 2.23 billion year duration includes the 'peak of galaxies' at (z=1.18) and is characterised in the absolute minimum of the quintessential lambda and the gravitational maximum contractions to form galactic structures and superstructures under the auspices of the Sarkar Constant of 236.1 million lightyears.

    Now looking back at those large redshift values, the lower one coinciding with the redshift of z=1.1 for supernova 1998 Iae, measured by Brian Schmidt of the 'High-Z-Team' must encompass a 'looking through' the imaged z-interval, namely the interval from the node at 2.23 billion years back to 4.46 billion years or the z-interval from
    (n=0.8676, v'/c=0.2867, z=0.3431) to (n=1.0000, v'/c=0.2500, z=0.2910).

    In other words, the 11D intersection of M-space intersects 10D-C-space in the two intervals, which form selfrelative images of each other.
    The 10D Riemann hypersphere is subject to gravitation in mass-parameters and decelerates asymptotically towards its 11D M-space boundary in negative and open curvature, mirroring the asymptotic expansion in perfect flatness of Euclidean zero curvature, however.
    The EMR-parameters so double themselves in the said interval, a interval which is itself expanding and contracts between the two nodal values of maximum frequency (fps) and minimum frequency (Ho).
    But it is only the EMR parameter that defines this 'oscillating universe', the mass parameter remains asymptotic as defined in the parametric scalefactor
    {r(n)=Rmax(n/(n+1), with Rmax=RHubble=RH=1.597767545x1026 m*}.

    Revisiting the redshift data of 1998, we notice the 'missing redshifts' in the interval from (z=0.12-0.3), with the limiting nodal (z=1.843) mapped onto the nodal (z=0.291) and the boundary image (z=1.082) mapped in its boundary image (z=0.343). The first supernova, beginning to 'curve away' from the decelerating expansion predicted by theory, is at about (z=0.12).
    Any receeding cosmological object with a redshift exceeding (z=0.291) can be considered to be moving in the 'Hubble Flow' with a measured redshift (zm=z), because after a distance of 2.23 billion ly no doubling of the electromagnetic parameters occurs for the distance between the two cosmic nodes.

    But we find three z-intervals, in whom we must apply a redshift-correction; set in the images of the boundaries and the nodes.
    The boundary (z=0.343, z=1.082) is imaged as the boundary image (zarp=0.2505, z=1.082) in the nodal mirror of (z=0.291, z=1.843) and the boundary mirror of (zarp=0.2505, z=1.082) images the nodal (z=0.291, z=1.843) in the nodal (z=zni, z=1.843).

    If (v'/c=0.22), then (zm=zarp=0.2505 as the variation maximum) and at the event horizon, where zm=0, the z(zm)=zarp and azm+b=0.291 for zm=zni; subsequently (b=zarp & azni=0.0405) and a the gradient of the 'Local Flow', given in the equation: (z(zm)=azm+0.2505) for the present epoch.

    The [Alpha]-Redshift spans the z(zm) range from (0.291 to 0.343) for the zm-interval from (zni to 0.2505) with positive gradient (0.052/(0.2505-zni)) and letting this gradient equal (a=0 from/zni) gives zni=0.1097 and (a=0.3692, for the [Alpha]-Redshift equation:
    (zred(zm)=0.3692(zm)+0.2505).

    The [Alpha]-Blueshift spans the zm-interval from (0.2505 to 0.2910) for the same range with a negative gradient ( -0.052/0.0405=-1.284) and a linear equation:
    (zblue(zm)=-1.284(zm)+0.6646).

    So the 'curving away' from the deceleration model at (z=1.12) becomes a consequence of the redshift (zni=0.1097) forming a nodal image in the other nodal redshifts of (z=0.291 and z=1.843); with the boundary redshift measured as (zm=0.2505), becoming a blueshift boundary for the interval until (zm=0.291), at which the true 'Hubble-Flow' begins at the present epoch with linear equation: (z(zm) = zm).

    The nearest, most studied and most luminous quasar (or quasi-stellar object) is called 'Q3C273' (Cambridge catalogue); its recessional velocity is measured as (v'/c=0.14565), for a (zm=0.1580).
    Applying the [Alpha]-Redshift equation gives a 'local flow correction' of: (z(0.1580)=0.3088), for which (n={√(c/v") -1}) and (v"/c=[(z2+2z)/(z2+2z+2)]) give corrected (n=0.9507) and (v"/c=0.2628).

    The distance to 'Q3C273' can now be calculated simply by the application of the scalefactor r(n) in 10 and 11 dimensions in the formulations:
    R10D(n) = r(np) - RH[n/(n+1)] and R11D(n) = [np - n]RH}
    'Q3C273' in 10D is (RH(0.53105 - 0.48736) = 0.044(16.88 billion ly) = 737.428 million ly);
    but in 11D this becomes: ([1.1324-0.9507]RH = 0.1817(0.53105)(16.88 billion ly) = 1.6288 billion ly).

    As the universal [Alpha]-Variation, the zarp redshift is the maximum variation for the present epoch in the Hubble-Oscillation and the fluctuation of the Hubble parameter as the cosmic frequency is mirrored about (H'o(np)=Ho/(2-np)), valid for the (n=1 to 2)-cycle; hence (H'o(np)= 58.04/0.8676=66.90 Hubble units).
    At the nodes, say at (np=2), (H'o) quantises as (fps) in the pixelation of spacetime.
    At the nodal images however, (H'o) would assume its nodal value of 58.04 Hubble Units.

    The Hubble 'Constant' subsequently varies with redshift at any cycletime (n); increasing from 58.04 to 66.9 in the z-intervals (0.1097-0.2505) and (0.2910-0.3431) and decreasing from 66.9 to 58.04 in the z-intervals (0.2505-0.2910) and (1.082-1.843) for the present Hubble epoch.
    The 'arpian redshift' as variation maximum is situated at n-coordinate 0.8676, implying that correctly interpreted spectroscopic measurements must converge at a Hubble-Constant of 66.9 Hubble units and a projected mapped age for the universe of (0.8676x16.88 billion years) or 14.65 billion years.
    For z=(0.3431-1.082), (Ho'=66.9) and the nodal intervals z=(0-0.110) and (z from 1.843) set it as (58.04).

    This is a simple yet profound solution to the 70-year search to finetune the 'Hubble-Constant'.
    It is no wonder, that there was so much disagreement regarding the measurements, seeing that it changes in the described intervals as a reflection of EMR parameters.
    All astronomical and cosmological measurements engage optical instruments to catch photons and all of astrochemistry and astrophysics depends on spectrum analysis.
    So the universe is 'well behaved' after all and decelerating under its own gravity, modified in the quintessence.

    But how do you explain the 25%, on average, discrepancy in the luminosity of the supernovae examined?

    That brings in the old 'Hubble Law', where the distance (RH) to an object receeding with velocity (v'=H'oxRH) sets an epoch dependent 'Hubble Constant' as the linear proportionality constant between recessional velocity and the distance to the object.
    In the case of the quasar 'Q3C273', the measured redshift (z=0.1580) relates a recessional velocity of (v'=0.14565c); which is then 'corrected' to calculate the n-cycle position of 'Q3C273', allowing a Hubble-independent determination of its distance from the observer.

    If you now use the applicable Hubble-Constant between (58.04 and 66.9) as (H'o=61.1 Hubble Units), interpolated say as:
    (H'o=66.9-[0.2505-0.1580][66.9-58.0]/(0.2505-0.1097) = 66.9-5.8 = 61.1 Hubble Units); then the old Hubble Law with (61.1 Hubble Units=1.98x10-18 1/s*) gives you:
    (RH= 0.14565c/H'o) and calculating as: (2.34 billion ly) and a distance 43% in excess of the n-cyclic value of (1.63 billion ly); but using a higher Hubble-Constant, such as 71 Hubble-Units, commonly used in the supernovae measurements, results in a scale reduction of 86% to (2.0 billion ly) and a 'dimming' effect of so 23%, which is the observed discrepancy.

    So the spectroscopic measurements incorporate a natural 'dimming effect' in luminosities, due to the cosmological objects, (which are physically much nearer, than their redshift indicate), appearing to be further away also in the electromagnetic universe, than they truly are and so the theoretical predictions of their distances are correct in principle, but require modification via the old Hubble Law, which is only approximate, (valid only at the odd nodes) and unnecessary to calculate the distances.
    And at higher redshifts, passing the imaging interval from (z=0.291 to 0.343), the seeming cosmic acceleration intensifies until the other imaging interval from (z=1.082 to 1.843) has been reached. The apparent cosmic acceleration hence becomes an imaged double boundary-nodal-mirror effect.

    The [Alpha]-Variation measures shifts in wavelength, which have passed through the described intervals and a 'dip' in the constant is derived from the mathematical analysis.
    How do you explain the magnitude of that dip; about 80 parts per million you said, in the light of the redshift intervals?

    The [Alpha]-Variation is the dimensional intersection of M-C-space, 10D-C-space forming a holographic image in 12D-F-space.
    The chargequantum (e) is defined via the Riemann Analysis of B(n), the supersymmetric wavefunction of the universe:
    {B(n) = [2e/hA]exp(-[Alpha]xT(n) Inverse Sorce energy or Magneto charge units (C*)}; where {T(n) =...- 3 - 2 - 1 +0+ 1 + 2 + 3 +...= n(n+1)} and the Feynman-Path-Integral for all particle histories as an alternative formulation to the Schrödinger- Dirac- and Klein-Gordon Equations for the quantum mechanistic probability distribution of quantum states in the particle-wave duality.

    The Action Law of (Action=ee*) manifests the lightspeed (c)-independent form of [Alpha] and can then be calibrated via the definition of the (c)-inclusive form in magnetic constant (μo). {[Alpha] = 60πe2/h = e2/(2εohc) = μoce2/(2h) = 1/137.0470731}

    A Newton-Raphson iteration for B(n) and the boundary condition {T(n)=i2 in B{-[1/2]+-i(½√3)}, with a first approximation: (e1=(½hA=1.618221145x10-19 C*) converges to: (e=1.606456344x10-19 C*).

    Abstract time in F-Space is defined as:

    N=Minimum Radius/Maximum Radius = λps/RHubble =λps/Rmax = nps

    and so allows the definition of Inverse Time as frequency parameter physicalizing this abstraction for time in modular mirror duality made manifest in the string epoch of the Inflaton.
    This then defines the GENESIS BOSON as the Particle of creation using the fundamental constants of Creation from the SEps algorithms. Those constants are then used inductively in the future by any sufficiently mentally evolved and cosmically selfaware civilisation to construct selfconsistent and logical measurement systems to rediscover their own nature and origins in a self induction of physical consciousness of their own cocreated Genesis in a perceived timearrow of entropy, flowing apparently from the past to the present to the future.

    In practical terms, this engages the measurement and analysis of two fundamental constants, namely the speed of light 'c' and the Planckian quantum constant 'h' to relate the quantum as a micro energy selfstate (eigenvalue) to what is termed the classical physics of macro selfstates exemplified in the theoretical physics of Newton, Maxwell and Einstein in scientific models of reality and encompassing mechanics, electromagnetism and the relativities respectively. The dimensional analysis of 'hc' as a energyxdisplacement parameter suffices to calibrate the unitary mensuration parameters for mass, displacement and time, say in the Terran System International or SI-system of measurements of fundamental quantities, say here the kilogram, the meter and the second respectively. The other elementary units ain the SI-system are derived from the algorithmic masterconstant set and comprise the Kelvin for temperature as kinetic measure of the quantum states, the Ampere and Coulomb for electric current, the mole for molarity , the candela for luminosity with the sterradian an additional geometrized unit for angular measures.

    Any arbitrary measurement system of an UO in a defined spacetime can then experimentally determine relationships and corollaries between experimental data and the changes in energy associated with dynamical systems. The UO has a mensuration system SI say and can calibrate its SI-system to any other unitary system like the star-* system of the UO*.


    Dimensional Unit Calibration:

    [m/s]/[m*/s*] = [c*/c] = [3x108/2.99792458x108] = [1.000692286] for {m/m*} = {1.000692286} {s/s*}​

    [Js]/[J*s*] = [h*/h] = [6.66666666..x10-34/6.62607004x10-34] = [1.006126803] for {J/J*} = {1.006126803} {s*/s}​

    [m5/s3]/[m5/s3]* = {[m/m*]2}.[c*/c]3 = Go*h*/Goh = 30ch*/30c*h = [c/c*][h*/h] = [0.999308193x1.00612803] = [1.005431984]​
    for {m/m*} = [c/c*]2.√[h*/h] = [0.998616864x1.00305872] = [1.001671357]​

    for {m}2 = 1.00334349 {m*}2 and m = 1.001671357 m* and m* = 0.998331431 m​

    s = {m/m*}.[0.999308193] s* = [1.001671357x0.999308193] s* = 1.000978394 s* and {m/s} = 1.000692286 {m/s}* for {m/s}2 = 1.00138505 {m*/s*}2 as c2

    J = {s*/s}[h*/h] J * = [0.999022562x1.006126803] J* = 1.005143377 J* and J* = 0.994882942 J​

    kg = {s*/s}.{s/m}2.{m*/s*}2.[h*/h] kg* = {s/s*}{m*/m}2.[h*/h] kg* = [1.000978394x0.996665646x1.006126803] kg* = 1.003753126 kg*​

    [H/m]/[H*/m*] = [J/J*][m*/m][C*/C]2.[s/s*]2 = μo*/μo = [120π/c*]/[4πx10-7]​
    for C = √{[Js/J*s*][m*s/ms*]} C* =√{[h*/h][c/c*]} C* = √[1.006126803/1.000692286] C* = 1.002711702 C*​

    [eV]/[eV*] = [e±J]/[e±J]* = [e±/e±*].[J/J*] for eV = [1.60217662x10-19/1.606456344x10-19].[1.005143377] eV* = 1.00246560 eV*​

    [J/K]/[J*/K*] = {J/J*}.{K*/K} = [k*/k] = [1.411721579x10-23/1.380649x10-23] = [1.022505777] for K = [J/J*]/[1.022505777] K* = [1.005143377/1.022505777] K*= 0.983020397 K*​


    Conversion Units are:​
    {s} = 1.000978394 {s*}​
    {m} =1.001671357 {m*}​
    {kg} = 1.003753126 {kg*}​
    {C} = 1.002711702 {C*}​
    {J} = 1.005143377 {J*}​
    {eV} = 1.00246560 {eV*}​
    {K} = 0.98301975 {K*}​

    (m*= 0.998331431 m; s*= 0.999022562 s ; kg*=0.99626091 kg) in calibration of the base masterconstants (h/h*, c/c*, [Go]u=(1/30c)) and we note the numerical constancy for the magnetic constant in both mensuration systems: (μo)=4πx10-7 Henry/m (H/m) in (SI) and (μo)=120π/c (H*/m*) in (*).​
    We recall that: (c=2.99792458x108 m/s (SI) and c*=3x108 m*/s* (*)).​
    The Henry is a derived (SI) unit for magnetic inductance and has base units (Js2/C2=kgm2/C2), which so must give the (C to C*) unitary calibration in (μoo*)=1=0.994598576 C*2/C2, which gives (C*=0.997295631C) and DEFINES the (SI)-Coulombic Charge quantum as: (e=0.997295631e*=1.6021119x10-19 C (SI)).​

    The textbooks of SI-physics have (e'=1.60217662x10-19 C (SI)), however and a value which differs from the value demanded by the magnetic constant (μo ) in a factor of (e'/e=1.0000403).
    As the electropolic charge quantum appears squared in the [Alpha]-Constant, the [Alpha]-variation so becomes (1.0000807), with the old value of (e') exceeding the new value of (e) in so 4 parts in 100,000 and [Alpha]' greater in magnitude than [Alpha] by 81 parts in a million and in agreement with the Churchill-Webb measurements of 1998, increasing from Alpha = μoc.e2/2h = 1/137.047075 to Alpha' = 1/137.036003.
    And I would suspect, that measuring [Alpha] even further back towards the Quantum Big Bang with increasing redshift, would better approximate the 80 parts per million increase in Alpha from say lower deviations at the say 8 parts per million at lower redshifts.

    So the '[Alpha]-Dip' indicates that the textbook value for the electropole is fractionally too high; but that the Alpha Finestructure-Constant remains indeed constant, once the variation in the electronic charge quantum is taken into account.
    Because the magnetic permeability constants are numerically the same in both the (SI) and the (*) unitary measurement systems; but
    εo = 1/120πc = 8.841941283x10-12 (F/m)* and is εo = 8.8541878176x10-12 F/m (SI), the (SI) measurement is too large by a factor of 1.00138505 to correlate correctly wirth the magnetic permeability constant μo to give the Maxwell constant μoo = (120π/c).(1/120πc) = 1/c2.

    It is experimentally measured in the (e/me)-ratio of the electron, subject to electric- and magnetic fields and this fits in nicely with my analysis of the electromagnetic mass of the electron.

    In particular, the effective mass of the electron: (me=h[Alpha]/(2πRec)=9.290528912x10-31 kg*), also contains a magnetocharged part via (e*=2Rec2) for ([Alpha]=meπe*/(hc)) in the unification of the EMI with the GI by [Go=4πεo]u.
    This magnetocharged part, intrinsic to the UFoQR as definition from (μo) and the quantisation of (λps) in (Re), we term 'Electromagnetic Mass':
    (meEMR = 2μoe2/(3Ree* = 1.556643x10-32 kg*)) which is subtracted from the effective mass (me), gives me = 9.134865x10-31 kg* or 9.10071x10-31 kg (SI) and in agreement with the SI-textbook value of 9.1093835x10-31 kg (SI) to 95 parts in 100,000, subject to perturbation theory in the factor 2/3 in the electromagnetic mass.

    The 'naked' restmass of the electron is about 98.245% of the effective mass, the latter specifying the 'naked' electron to move with a speed of (0.18077c) through an electric potential of (8.5748 keV*).
    A detailed analysis of the electron's relativistic mass increase in equality with its energy of magnetic self induction forms the mathematical basis to 'prove' the 'Theory of Quantum Relativity' via a binomial distribution of the (v/c) parameter about the (X+Y=XY=i2=exp[iπ]= -1) FRB or 'Functional Riemann Bound' in a 'Complex Riemann Analysis'.
    The '[Alpha]-Dip' is like a double symmetry; the magneto charged part of the electron is hidden and une requires the 'image of the image' to notice the skewing of the experimental data. The [Alpha]-Variation provides the mirroring of the nodes in the boundaries and vice versa and so indicates the intrinsic definition of the [Alpha]-Finestructure-Constant as the manifestation of the interdimensional law of action, leading to a 4-dimensional superconductivity coupled to the vacuum or zero-point-energy.

    In the attempt to explain the [Alpha]-Dip, some theoretists have proposed a 'slowing down' of (c).
    Recent formulations by populist physicist Paul Davies and in co-authorship with Tamara Davis and Charles Lineweaver from the Department of Astrophysics at the University of New South Wales, Sydney, Australia have followed the wrong avenues for the interpretation of the data however.
    In a paper published in ('Nature': 'Black Holes constrain varying constants'; August 8th, 2002), the authors propose a varying light speed to be responsible for the [Alpha]-Dip and discount any possible variation in the electro charge quantum.

    Davies' argument that an increase in (e) would alter the evolution of Black Holes in their entropic definitions does not take into account that a productation of the Boltzmann Constant (defining entropy), with (e) forms a fundamental finestructured constant in its own right.

    In particular, the universe's wavefunction B(n) is localised in any arbitrary spacetime in 'unfreezing' the M-space 'stuck' in between the (X,Y) coordinates and subsequently in between real and imaginary linearised time parameters. This demands the establishment of a Mean-Alignment-Time or MAT, relative to a 'unfreezing definition' in a specification of the 'naked singularity', oscillating as zero-point about the FRB.

    As E*.e= Epsx1/Eps = 1 as fundamental unity in the 11D Membrane-Mirror-Space of modular duality with e* the magneto charge; one can heuristically state that
    (Energy E x charge quantum e) in the lower dimensional C-Line-Space C can be expressed as the inversed identity in the form of 1/T.
    This then sets E.e=kTe=1 for [ek]=1/T and using an inverse proportion for mass in the lower dimensionality: [e*k*] = 1/T* sets a function f(n) = [ek]/[e*k*] = [T*/T].

    This is the case for the Mass-Temperature inverse proportionality for the evolution of Black Holes from micro states to macro states and as in the Hawking Mass-Temperature relation for Black Holes:

    {Minimum Planck Oscillator = ½hfPlanck = ½mPlanck.c2 for Tmax=Tps and Tmin=Tss in string modular T-duality for[/indent]
    ½mPlanck.TPlanck = (1/8π)(4π).mPlanck.TPlanck = Hawking Modulus HM = hc3/4πGok = MBHmin.TBHmax ={c2/4π2}. MBHmax.TBHmin.}.

    friedmann6. friedmann9.

    B(n) is assigned B(np) = {[ek](SI)/[ek](*)}, with {[ek](SI)=constant=(1.60217662x10-19 C)(1.380649x10-23 J/K) = 2.21204355x10-42 CJ/K} and using the old (SI) value with the Alpha-Variation for (e'); using (e±=1.6021119x10-19 C) without the Alpha-Variation gives {[ek](SI)} = 2.21195419x10-42 CJ/K}.


    decepar3-.44442.
    The (*)-constant is a relatively fixed constant as: (e±*k*=2.267869086x10-42 (CJ/K)*) and subsequently B(np) calculates a particular value for n at the asymptote B(n⇒±∞)=0 as:

    {[e±k](SI)/[e±k]*} = (2.21204355/2.267869086) = 0.975384145 (0.975344742)= [2e/hA].exp(-[Alpha]x[np2+np]), which yields an unique (np) as a complex solution to the quadratic equation by ln(0.975384145/0.992729803) = {ln(0.982527312)/-Alpha} = 2.415747501 = np2+np for: np2 + np - 2.415747501 = 0
    solving as: (np=FRB(-½) ± 1.6327117).
    For the unfrozen M-space with Alpha-Variation: {10D-root: np = 1.1327117 (real) & 12D-root: np = -2.1327117 (imaginary)}.
    For the unfrozen M-space without Alpha-Variation: {10D-root: np = 1.1344063 (real) & 12D-root: np = -2.1344063 (imaginary)}.

    This 'unfreezing' of M-space then allows the singularity algorithm of the cosmogenesis to manifest in what might be called the sex chromosomes of the universal DNA-encoding in terms of frequency or a number count.

    A new physical quantity in 'awareness' is defined as the timedifferential of frequency and allows the concept of 'consciousness' to be born from the defining qualities of magneto charges.
    Electromagneto-monopolic 'Life' derives as consequence of selfinductions of quantum geometric entities, specified from super membranes, macro-crystallised in electropolic self-capacitances and magnetopolic self-inductances, subsequently becoming subject to mutual cross inductances.
    The purpose of the superbranial selfreplication on ever increasing scales, and until modular duality is reached in minmax boundary conditions; is to establish the multiversal nestings of the smallest within the largest - a process which constituted the beginnings of it all in the 'naked singularity' becoming defined as the Genesis BOSON.


    The GENESIS Boson then becomes the parametric initialisation of creation in the abstract labelings of:
    ENERGY=k.TEMPERATURE=h.FREQUENCY=h/TIME=MASS.c2 and using the SEps-MasterConstant Set: {4; 6; 7; Lo=1/[6x1015]; c2=9x1016; 11; h=1/[15x1032]; A=14x1524; k=1/[15x1618]; 26x6561} in reverse order and with arbitrary symbols as shown becoming associated with those 'master constants'.

    Particularly then: ENERGY=hRmaxps with MASS=hRmaxpsc2=0.01183463299 and TEMPERATURE=hRmax/kλps=7.544808988..x1037 and FREQUENCY=Rmaxps=1.59767545..x1048

    This becomes the 'Atomic-Mass-Unit' in 12D-F-Space in using one protonucleon mc=Alpha9Lplanck for every one of the 12 monopolar current loops in the Unified Field of Quantum Relativity (UFoQR).
    A first Eps-Coefficient in the Expansion Series of the fundamental priciples from the SEps algorithm then crystallizes the 'Counter for matter' in Avogadro's Constant for Molarity:
    MASS(20/33)/12mc = Navogadro = 6.02242143x1023 1/mol*

    N=npsps/Rmax in REAL Time relative to the Quantum Big Bang to be created following the string epoch and relating to IMAGINARY TIME relative to this selfsame creation in the Cosmogony of the Genesis Boson of the Abba-Baab 11-dimensional supermembrane. This UNREAL Quantum Relative Time then is the Hubble-FREQUENCY Ho=c/Rmax in proportionality to the Source Frequency of the Eps-Gauge Photon fps=c/λps in the expression HoRmax=c=λps.fps

    N then becomes the Nulltime for the initialisation of the string/supermembrane-serpent modular duality in the De Broglie phasespeed initialisation, beginning with the Oscillation (or Bounce) of the Planck-Length and specifies the Instantenuity of Now-Cycle-Time nps=Hotps=Ho/tss as the Time Instanton tps=1/fps=fss and the Inflaton Rmax=RHubble=c/Ho with de Broglie Phasespeed Vdebroglie=Rmax.fps=Rmax.c/λps=c/nps as the 'Heartbeat of the Cosmic Mother Black Hole' frequency of the oscillating cosmos in the Cosmology of QR and in the imaginary F-Space Time of NHo generalised in the Real Time n=Hot for any time in the evolving Cosmology and minimised in nps=Hotps.

    L(nps,T(nps) = 6π2λps2.σ.T4 = 2.6711043034x1096 Watts*, where σ = Stefan's Constant = 2π5k4/15h3c2 and as a product of the defined 'master constants' k, h, c2, π and 'e'.


    L(n,T) = 3HoMo.c2/550n and for Temperature T(nps)
    T(nps) = 2.93515511x1036 Kelvin*.

    This manifests as a 'false vacuum' and as a temperature gradient, as a causation of the Big Bang Instanton on physical grounds.
    The metaphysical ground is the symmetry breaking from the source parity violation described in the birth and necessity of the Graviton to resymmetrize the UFoQR.
     
    Last edited: Feb 26, 2018
  5. admin

    admin Well-Known Member Staff Member

    Messages:
    3,158
    2. The Inflaton

    SEWG-------------SEWg---SEW.G---SeW.G---S.EW.G------S.E.W.G
    Planck Unification I----------IIB----------HO32------------IIA-----------HE64---------Bosonic Unification

    2.1 Graviton Unification in Monopole Class IIB
    SEWG ---- SEWg as string transformation from Planck brane to (Grand Unification/GUT) monopole brane

    String-BosonDecoupling Time s* Wavelength (λ=2πl) m*Energy (hc/λ) J* & eV*Modular Wavelength m*Temperature
    K*
    Significance
           
    1. Planck-Boson
    I/SEWG
    tP=2πrP/c
    4.377x10-43
    1.313x10-341.523 GJ* or 9.482x1027 eV*7.617x10331.079x1032 Outside Hubble Horizon Limit in Protoverse
    2. Monopole-Boson
    IIB/SEWg
    GI-GUT decoupling
    tM=2πrM/c
    1.537x10-40
    4.6110x10-324.337 MJ* or 2.700x1025 eV*2.169x10313.072x1029Outside Hubble Horizon Limit in Protoverse
    3. XL-Boson
    HO32/SEW.G
    tXL=2πrXL/c
    2.202x10-39
    6.605x10-31302.817 kJ* or 1.885x1024 eV*1.514x10302.145x1028Outside Hubble Horizon Limit in Protoverse
    4. ECosmic Bosons
    IIA/SeW.G
    SNI decoupling
    tEC=2πrEC/c
    6.717x10-34
    2.015x10-250.9927 J* or 6.180x1018 eV*4.964x10247.032x1022Galactic Supercluster Sarkar
    Mo=RSarkarc2/2Go Scale
    5. False Higgs VacuumtHiggsPE=2πrHiggsPE/c
    tps.T(nps)/Talgo
    1.297x10-32
    3.891x10-240.0514 J* or 3.200x1017 eV*2.570x10233.641x1021Galactic Supercluster Scale
    6. Weyl-Boson
    HE64/S.EW.G
    Big Bang-Instanton
    EMI decoupling
    tps=2πrps/c
    3.333x10-31
    1.000x10-220.002 J* or 1.245x1016 eV*1.000x10221.417x1020Galactic Halo(Group) Scale
    7. T(n)=Tps
    Bosonic Unification
    tBU=nBU/Ho
    1.897x10-9
    0.56902
    Protoverse
    T(n)4 = {[n+1]2/n3}HoMoc2/(2π2sRH2[550]) = 18.1995{[n+1]2/n3} (K4/V)*1.757
    Protoverse

    Tps-bosonic
    TEW4=
    18.2[n+1]2/n3
    n=HotBU
    Unitary Modular Geometric Mean Scale
    8. Higgs Boson Vacuum
    Electroweak WNI decoupling
    tEW=nEW/Ho
    0.00274~1/365
    4.167x10-18
    Quantum Scale
    4.799x10-8 J* or 298.785 GeV*2.400x10173.400x1015Inner Mesonic Ring Quantum Scale
    The Coupling of the Supermembranes in Vafa-F-Space of Inflaton Selfdual Monopole IIB

    We next reduce the atomic scaling to its intrinsic superstring dimension in deriving the Higgs Bosonic Restmass Induction, corresponding to the Dilaton of M-Theory.

    Renormalising the wavefunction B(n) about the FRB=-½ as maximum ordinate gives a probability y2dV for y(0)=√(alpha/2π) for the renormalization.

    Alpha/2π being the probability of finding the FRB fluctuation for the interval [-X,X-1] in volume element dV as the uncertainty fluctuation.
    This volume element defines the dimensional intersection from C-Space into F-Space via M-Space in the topological mapping of the complex Riemann C-Space about the Riemann pole of the FRB as the Calabi-Yau superstring space in 10 dimensions.


    X=½(√5-1)=0.618033..... and Y=-(X+1)=-½(√5+1)=-1.618033...

    -X(X-1)=0.236067... in analogue to X(X+1)=1=T(n) and XY=X+Y=-1=i2 as the complex origin.

    But 0.236067..= X3, so defining the 'New Unity' as #3=Alpha and the precursive unity as the Cuberoot of Alpha or as # in the symmetry #:#3 = SNI:EMI = Strong Nuclear Interaction Strength { ElectroMagnetic Interaction Strength}.

    The Strong-Interaction-Constant SIC=√Alpha=√e2/2εohc=√(60πe2/h) in standard and in string units, reduces the SNI finestructure constant # by a factor Alpha1/6 ; that is in the sixth root of alpha and so relates the SIC at the post quantisation level as # to the pre-quantum epoch as SIC=√Alpha=#3/2.

    The SNI is therefore so 11.7 times weaker at the XL-Boson 'Grand-Unification-Time' SEW.G of heterotic superstring class HO(32), than at the EpsEss time instantenuity S.EW.G of the superstring of the Quantum Big Bang in heterotic class HE(8x8) {this is the stringclass of Visi in the group theories}.
    This then is the Bosonic Gauge Coupling between superstrings HO(32) and HE(8x8).

    The coupling between superstrings IIA (ECosmic and manifesting the cosmic rays as superstring decay products) and IIB (Magnetic Monopole) derives directly from the B(n), with B(n=0)=Jo=2e/hA = 0.9927298 1/J* or 6.2705x109 GeV* and representative of the ECosmic stringclass and the super high energy resonances in the cosmic ray spectrum, bounded in the monopolic resonance limit of 2.7x1016 GeV*.

    1-Jo=0.00727021 approximates ρg/c2=4/550=0.007272... approximates Alpha at n=nps.

    The Unity of the SNI transforms to [1-X]=X2 and the EMI transforms as the Interaction of Invariance from X to X.
    The Weak Nuclear Interaction or WNI as X2 becomes [1+X]=1/X and the Gravitational Interaction or GI transforms as X3 transforms to [2+X]=1/X2 by MODULAR SYMMETRY between X and Alpha and the encompassing Unification Unity: [1-X][X][1+X][2+X] = 1.

    This Unification Polynomial U(u)=u4+2u3-u2-2u+1 = 0 then has minimum roots (as quartic solutions) at the Phi=X and the Golden Mean Y=-(1+X).

    This sets the coupling between SNI and EMI as X; the coupling between EMI and WNI becomes X2 and the coupling between WNI and GI then is again X.
    The general Force-Interaction-Ratio so is: SNI:EMI:WNI:GI = SEWG = #:#3:#18:#54.

    This is the generalisation for the cubic transform: x→x3 with the Alpha-Unity squaring in the functionality of the WNI and defining G-Alpha as Alpha18 in the Planck-Mass transforming in string bosonic reduction to a basic fundamental nucleonic mass (proton and neutrons as up-down quark conglomerates and sufficient to construct a physical universe of measurement and observation):

    mc=mplanck Alpha9 from the electromagnetic string unification with gravitation in the two dimensionless finestructures:

    For Gravitational Mass Charge from higher D Magnetic Charge: 1=2πG.mplanck2/hc

    For Electromagnetic Coulomb Charge as lower D Electric Charge: Alpha=2πke2/hc

    Alpha as the universal masterconstant of creation, then becomes defined via the Riemann Analysis from XY=i2 definition, reflecting in modulation in the statistical renormalisation of the B(n) as the probability distributions in quantum wave mechanics however.U(u) has its maximum at u=-½=FRB for U(-½)=25/16=(5/4)2 for the B(n) supersymmetry.

    The derivation of the HBRMI draws upon this definition process and sets the coupling angle as arcsin(X/@) for a Unitary 'Force' @=(#fG).cfpsE-Alpha/Alpha and with the electron mass replacing the fundamental nucleonmass mc in the definition of E-Alpha.

    A disassociated GI unifies with the WNI in the L-Boson and is supersymmetric to an intrinsic unification between the SNI and the EMI as the X-Boson for the duality fGfS=1 in modular definition of a characteristic GI-mass #fG as the disassociated elementary gauge field interaction.

    The transformation of the 5 superstring classes proceeds in utilizing the self-duality of superstring IIB as the first energy transformation of the Inflaton in the Planck string class I transmutating into the monopole string class IIB.

    uni2-.37328.
    xlboson.


    ufoqrpdf.

    ufoqr1.

    2.2 Quark-Lepton Unification in XL-Boson Class HO(32)
    SEWg --- SEW.G

    higgs1.
    higgs2.


    2.3 Cosmic Ray Unification in XL-Boson Class IA
    SEW.G --- SeW.G


    The Elementary Cosmic Ray Spectrum

    The elementary Cosmic Ray Spectrum derives from the transformation of the Planck-String-Boson at the birth of the universe.

    The following tabulation relates those transformation in energy and the modular duality between the distance parameters of the macrocosm of classical spacetime geometry and the microcosm of the quantum realm.

    String-BosonWavelength (λ) mEnergy (hc/λ) J & eVModular Wavelength mSignificance
    1. Planck-Boson1.2x10-34 m1.6 GJ or 9.9x1027 eV8.0x1033 mOutside Hubble Horizon Limit
    2. Monopole-Boson4.6x10-32 m4.3 MJ or 2.7x1025 eV2.2x1031 mOutside Hubble Horizon Limit
    3. XL-Boson6.6x10-31 m303 kJ or 1.9x1024 eV1.5x1030 mOutside Hubble Horizon Limit
    4. X-K-Boson transit (+)8.8x10-28 m227 J or 1.6x1021 eV1.1x1027 m2πRHubble11D
    5. X-K-Boson transit (-)1.0x10-27 m201 J or 1.2x1021 eV1.0x1027 m2πRHubbleHorizonLimit
    6. CosmicRayToe1.9x10-27 m106 J or 6.6x1020 eV5.3x1026 m2πRHubble10D
    7. CosmicRayAnkle2.0x10-25 m1.0 J or 6.2x1018 eV5.0x1024 mGalactic Supercluster Scale
    8. CosmicRayKnee (+)1.0x10-22 m0.002 J or 1.24x1016 eV1.0x1022 mGalactic Halo(Group) Scale
    9. CosmicRayKnee (-)6.3x10-22 m0.3 mJ or 2.0x1015 eV1.6x1021 mGalactic Disc(Halo) Scale
    10.CosmicRay1.4x10-20 m0.002 mJ or 1.4x1013 eV7.1x1019 mGalactic Core Scale
    Lower Cosmic Ray energies then become defined in standard physics, such as supernovae, neutron stars and related phenomena, engaging electron accelerations and synchrotron radiation.

    7. represents the ECosmic-Boson aka superstring class IIA as a D-brane attached open string dual to the (selfdual) monopole string class IIB and where the D-Brane or Dirichlet-Coupling in both cases becomes the 'intermediary' heterotic (closed loop) superstring HO(32).
    It is the HO(32) superstring, which as a bosonic full-quantum spin superstring bifurcates into the subsequently emerging quark-lepton families as the K-L-Boson split into Proto-DiNeutronic Ylemic NeutronMatter.
    The Ylem then manifests the massless Higgs Bosonic precursor as a scalar 'Neutron-Boson' (10), which then becomes massinductive under utility of the Equivalence Principle of General Relativity, relating gravitational mass to inertial mass.

    It are supersymmetric double neutrons which bifurcate into the observed mass content in the universe and not a decoupling matter-antimatter symmetry.
    The primordial neutron beta-decay so manifests the nucleon-lepton distinction in the decoupling of the strongweak nuclear interaction, mediated by the electromagnetic alpha-interaction hitherto unified with the omega-gravitational interaction. This primordial ylem radioactivity manifests the bosonic string class IIB as a monopolic masscurrent as a D-brane interaction in modular duality to the transformation of the selfdual magnetic monopole to the bi-dual electromagnetic cosmic rays at the ECosmic energy level.
    The monopole class is chiral (selfdual) and the Ecosmic class is nonchiral (bi-dual); from this derives the nonparity of the spacial symmetry aka the CP-Violation of the weak nuclear interaction, related to neutrinoflux as monopolic superconductive currentflows.

    As the heterotic classes are all 'closed looped', the elementary particles of the standard models emerge from the HE(64) class coupled to the HO(32) class in the inflationary string epoch.

    8. depicts the Weyl-Boson of the Big Bang Planck-singularity of the Weyl-Geodesic of relativistic spacetime as the final 'octonionised' string class HE(8x8).

    9. modulates the experimentally well measured 'knee' energy for Cosmic Rays as the distribution flux of high-energy protons as the primary particle in the 2π-factor. The wormhole radius is 10-22 m/2π for a Halo-(DarkMatter)-Radius of 2πx1022 metres.

    10. is the massless ancestor of the Higgs-template and defined through the Weyl-String-Eigenenergy E*=kT*=hf*=m*c2 =1/e*=1/2Re c2.
    The scale of (10) emerges from the holographic principle as 2π2R*3.f*2=e* for R*=h/(2πm'c)=1.41188..x10-20 m for a Compton Energy of E'=m'c2=2.2545..x10-6 J or 14.03 TeV, which serendipitously is the maxium energy regime for which the LHC is designed.

    The Experimental Evidence for the Superstrings is observed indeed every day in the laboratories of the astrophysics around the globe.


    The SciAm article below from 1998 links to the above in clarification of the questions raised.

    http://auger.cnrs.fr/presse/ScAm_jan97.html

    Cosmic Rays at the Energy Frontier

    cosmicray1.
    The Life of a Cosmic Ray


    These particles carry more energy than any others in the universe. Their origin is unknown but may be relatively nearby.

    by James W. Cronin, Thomas K. Gaisser and Simon P. Swordy


    Roughly once a second, a subatomic particle enters the earth's atmosphere carrying as much energy as a well-thrown rock. Somewhere in the universe, that fact implies, there are forces that can impart to a single proton 100 million times the energy achievable by the most powerful earthbound accelerators. Where and how?
    Those questions have occupied physicists since cosmic rays were first discovered in 1912 (although the entities in question are now known to be particles, the name "ray" persists). The interstellar medium contains atomic nuclei of every element in the periodic table, all moving under the influence of electrical and magnetic fields. Without the screening effect of the earth's atmosphere, cosmic rays would pose a significant health threat; indeed, people living in mountainous regions or making frequent airplane trips pick up a measurable extra radiation dose.

    cosmicray2.
    Cosmic-Ray
    Accelerator


    Perhaps the most remarkable feature of this radiation is that investigators have not yet found a natural end to the cosmic-ray spectrum. Most well-known sources of charged particles--such as the sun, with its solar wind--have a characteristic energy limit; they simply do not produce particles with energies above this limit. In contrast, cosmic rays appear, albeit in decreasing numbers, at energies as high as astrophysicists can measure. The data run out at levels around 300 billion times the rest-mass energy of a proton because there is at present no detector large enough to sample the very low number of incoming particles predicted.
    Nevertheless, evidence of ultrahigh-energy cosmic rays has been seen at intervals of several years as particles hitting the atmosphere create myriad secondary particles (which are easier to detect).

    On October 15, 1991, for example, a cosmic-ray observatory in the Utah desert registered a shower of secondary particles from a 50-joule (3 x 1020 electron volts) cosmic ray. Although the cosmic-ray flux decreases with higher energy, this decline levels off somewhat above about 1016 eV, suggesting that the mechanisms responsible for ultrahigh-energy cosmic rays are different from those for rays of more moderate energy.
    In 1960 Bernard Peters of the Tata Institute in Bombay suggested that lower-energy cosmic rays are produced predominantly inside our own galaxy, whereas those of higher energy come from more distant sources. One reason to think so is that a cosmic-ray proton carrying more than 1019 eV, for example, would not be deflected significantly by any of the magnetic fields typically generated by a galaxy, so it would travel more or less straight. If such particles came from inside our galaxy, we might expect to see different numbers coming from various directions because the galaxy is not arranged symmetrically around us. Instead the distribution is essentially isotropic, as is that of the lower-energy rays, whose directions are scattered.


    Supernova Pumps

    Such tenuous inferences reveal how little is known for certain about the origin of cosmic rays. Astrophysicists have plausible models for how they might be produced but no definitive answers. This state of affairs may be the result of the almost unimaginable difference between conditions on the earth and in the regions where cosmic rays are born. The space between the stars contains only about one atom per cubic centimeter, a far lower density than the best artificial vacuums we can create. Furthermore, these volumes are filled with vast electrical and magnetic fields, intimately connected to a diffuse population of charged particles even less numerous than the neutral atoms.

    This environment is far from the peaceful place one might expect: the low densities allow electrical and magnetic forces to operate over large distances and timescales in a manner that would be quickly damped out in material of terrestrial densities. Galactic space is therefore filled with an energetic and turbulent plasma of partially ionized gas in a state of violent activity. The motion is often hard to observe on human timescales because astronomical distances are so large; nevertheless, those same distances allow even moderate forces to achieve impressive results. A particle might zip through a terrestrial accelerator in a few microseconds, but it could spend years or even millennia in the accelerator's cosmic counterpart. (The timescales are further complicated by the strange, relativity-distorted framework that ultrahigh-energy cosmic rays inhabit. If we could observe such a particle for 10,000 years, that period would correspond to only a single second as far as the particle is concerned.)

    Astronomers have long speculated that the bulk of galactic cosmic rays--those with energies below about 1016 eV--originate with supernovae. A compelling reason for this theory is that the power required to maintain the observed supply of cosmic-ray nuclei in our Milky Way galaxy is only slightly less than the average kinetic energy delivered to the galactic medium by the three supernova explosions that occur every century. There are few, if any, other sources of this amount of power in our galaxy.

    When a massive star collapses, the outer parts of the star explode at speeds of up to 10,000 kilometers per second and more. A similar amount of energy is released when a white dwarf star undergoes complete disintegration in a thermonuclear detonation. In both types of supernovae the ejected matter expands at supersonic velocities, driving a strong shock into the surrounding medium. Such shocks are expected to accelerate nuclei from the material they pass through, turning them into cosmic rays. Because cosmic rays are charged, they follow complicated paths through interstellar magnetic fields. As a result, their directions as observed from the earth yield no information about the location of their original source.

    By looking at the synchrotron radiation sometimes associated with supernova remnants, researchers have found more direct evidence that supernovae can act as accelerators. Synchrotron radiation is characteristic of high-energy electrons moving in an intense magnetic field of the kind that might act as a cosmic-ray accelerator, and the presence of synchrotron x-rays in some supernova remnants suggests particularly high energies. (In earthbound devices, synchrotron emission limits a particle's energy because the emission rate increases as a particle goes faster; at some point, the radiation bleeds energy out of an accelerating particle as fast as it can be pumped in.) Recently the Japanese x-ray satellite Asca made images of the shell of Supernova 1006, which exploded 990 years ago. Unlike the radiation from the interior of the remnant, the x-radiation from the shell has the features characteristic of synchrotron radiation. Astrophysicists have deduced that electrons are being accelerated there at up to 1014 eV (100 TeV).

    The EGRET detector on the Compton Gamma Ray Observatory has also been used to study point sources of gamma rays identified with supernova remnants. The observed intensities and spectra (up to a billion electron volts) are consistent with an origin from the decay of particles called neutral pions, which could be produced by cosmic rays from the exploding star's remnants colliding with nearby interstellar gas. Interestingly, however, searches made by the ground-based Whipple Observatory for gamma rays of much higher energies from some of the same remnants have not seen signals at the levels that would be expected if the supernovae were accelerating particles to 1014 eV or more.

    A complementary method for testing the association of high-energy cosmic rays with supernovae involves the elemental composition of cosmic-ray nuclei. The size of the orbit of a charged particle in a magnetic field is proportional to its total momentum per unit charge, so heavier nuclei have greater total energy for a given orbit size. Any process that limits the particle acceleration on the basis of orbit size (such as an accelerating region of limited extent) will thus lead to an excess of heavier nuclei at high energies.
    Eventually we would like to be able to go further and look for elemental signatures of acceleration in specific types of supernovae. For example, the supernova of a white dwarf detonation would accelerate whatever nuclei populate the local interstellar medium. A supernova that followed the collapse of a massive star, in contrast, would accelerate the surrounding stellar wind, which is characteristic of the outer layers of the progenitor star at earlier stages of its evolution. In some cases, the wind could include an increased fraction of helium, carbon or even heavier nuclei.

    The identity of high-energy cosmic rays is all but lost when they interact with atoms in the earth's atmosphere and form a shower of secondary particles. Hence, to be absolutely sure of the nuclear composition, measurements must be made before the cosmic rays reach dense atmosphere. Unfortunately, to collect 100 cosmic rays of energies near 1014 eV, a 10-square-meter detector would have to be in orbit for three years. Typical exposures at present are more like the equivalent of one square meter for three days.

    Researchers are attacking this problem with some ingenious experiments. For example, the National Aeronautics and Space Administration has developed techniques to loft large payloads (about three tons) with high-altitude balloons for many days. These experiments cost a tiny fraction of what an equivalent satellite detector would. The most successful flights of this type have taken place in Antarctica, where the upper atmosphere winds blow in an almost constant circle around the South Pole.
    A payload launched at McMurdo Sound on the coast of Antarctica will travel at a nearly constant radius from the Pole and return eventually to near the launch site. Some balloons have circled the continent for 10 days. One of us (Swordy) is collaborating with Dietrich Müller and Peter Meyer of the University of Chicago on a 10-square-meter detector that could measure heavy cosmic rays of up to 1015 eV on such a flight. There are efforts to extend the exposure times to roughly 100 days with similar flights nearer the equator.

    cosmicray3.
    High-Altitude
    Balloon



    Across Intergalactic Space

    Studying even higher-energy cosmic rays--those produced by sources as yet unknown--requires large ground-based detectors, which overcome the problem of low flux by watching enormous effective areas for months or years. The information, however, must be extracted from cascades of secondary particles--electrons, muons and gamma rays--initiated high in the atmosphere by an incoming cosmic-ray nucleus. Such indirect methods can only suggest general features of the composition of a cosmic ray on a statistical basis, rather than identifying the atomic number of each incoming nucleus.

    At ground level, the millions of secondary particles unleashed by one cosmic ray are spread over a radius of hundreds of meters. Because it is impractical to blanket such a large area with detectors, the detectors typically sample these air showers at a few hundred or so discrete locations.
    Technical improvements have enabled such devices to collect increasingly sophisticated data sets, thus refining the conclusions we can draw from each shower. For example, the CASA-MIA-DICE experiment in Utah, in which two of us (Cronin and Swordy) are involved, measures the distributions of electrons and muons at ground level. It also detects Cerenkov light (a type of optical shock wave produced by particles moving faster than the speed of light in their surrounding medium) generated by the shower particles at various levels in the atmosphere. These data enable us to reconstruct the shape of the shower more reliably and thus take a better guess at the energy and identity of the cosmic ray that initiated it.
    The third one of us (Gaisser) is working with an array that measures showers reaching the surface at the South Pole. This experiment works in conjunction with AMANDA, which detects energetic muons produced in the same showers by observing Cerenkov radiation produced deep in the ice cap. The primary goal of AMANDA is to catch traces of neutrinos produced in cosmic accelerators, which may generate upward-streaming showers after passing through the earth.

    In addition to gathering better data, researchers are also improving detailed computer simulations that model how air showers develop. These simulations help us to understand both the capabilities and the limitations of ground-based measurements. The extension to higher energies of direct cosmic-ray detection experiments, which allows both ground-based and airborne detectors to observe the same kinds of cosmic rays, will also help calibrate our ground-based data.


    Rare Giants

    Cosmic rays with energies above 1020 eV strike the earth's atmosphere at a rate of only about one per square kilometer a year. As a result, studying them requires an air-shower detector of truly gigantic proportions. In addition to the 1991 event in Utah, particles with energies above 1020 eV have been seen by groups elsewhere in the U.S., in Akeno, Japan, in Haverah Park, U.K., and in Yakutsk, Siberia.
    Particles of such high energy pose a conundrum. On the one hand, they are likely to come from outside our galaxy because no known acceleration mechanism could produce them and because they approach from all directions even though a galactic magnetic field is insufficient to bend their path. On the other hand, their source cannot be more than about 30 million light-years away, because the particles would otherwise lose energy by interaction with the universal microwave background--radiation left over from the birth of the cosmos in the big bang. In the relativistic universe that the highest-energy cosmic rays inhabit, even a single radio-frequency photon packs enough punch to rob a particle of much of its energy.

    If the sources of such high-energy particles were distributed uniformly throughout the cosmos, interaction with the microwave background would cause a sharp cutoff in the number of particles with energy above 5 x 1019 eV, but that is not the case. There are as yet too few events above this nominal threshold for us to know for certain what is going on, but even the few we have seen provide us with a unique opportunity for theorizing. Because these rays are essentially undeflected by the weak intergalactic magnetic fields, measuring the direction of travel of a large enough sample should yield unambiguous clues to the locations of their sources.

    It is interesting to speculate what the sources might be. Three recent hypotheses suggest the range of possibilities: galactic black-hole accretion disks, gamma-ray bursts and topological defects in the fabric of the universe.
    Astrophysicists have predicted that black holes of a billion solar masses or more, accreting matter in the nuclei of active galaxies, are needed to drive relativistic jets of matter far into intergalactic space at speeds approaching that of light; such jets have been mapped with radio telescopes. Peter L. Biermann of the Max Planck Institute for Radioastronomy in Bonn and his collaborators suggest that the hot spots seen in these radio lobes are shock fronts that accelerate cosmic rays to ultrahigh energy. There are some indications that the directions of the highest-energy cosmic rays to some extent follow the distribution of radio galaxies in the sky.

    The speculation about gamma-ray bursts takes off from the theory that the bursts are created by relativistic explosions, perhaps resulting from the coalescence of neutron stars. Mario Vietri of the Astronomical Observatory of Rome and Eli Waxman of Princeton University independently noted a rough match between the energy available in such cataclysms and that needed to supply the observed flux of the highest-energy cosmic rays. They argue that the ultrahigh-speed shocks driven by these explosions act as cosmic accelerators.

    Perhaps most intriguing is the notion that ultrahigh-energy particles owe their existence to the decay of monopoles, strings, domain walls and other topological defects that might have formed in the early universe. These hypothetical objects are believed to harbor remnants of an earlier, more symmetrical phase of the fundamental fields in nature, when gravity, electromagnetism and the weak and strong nuclear forces were merged. They can be thought of, in a sense, as infinitesimal pockets preserving bits of the universe as it existed in the fractional instants after the big bang.
    As these pockets collapse, and the symmetry of the forces within them breaks, the energy stored in them is released in the form of supermassive particles that immediately decay into jets of particles with energies up to 100,000 times greater than those of the known ultrahigh-energy cosmic rays. In this scenario the ultrahigh-energy cosmic rays we observe are the comparatively sluggish products of cosmological particle cascades.

    Whatever the source of these cosmic rays, the challenge is to collect enough of them to search for detailed correlations with extragalactic objects. The AGASA array in Japan currently has an effective area of 200 square kilometers, and the new Fly's Eye HiRes experiment in Utah will cover about 1,000 square kilometers. Each detector, however, can capture only a few ultrahigh-energy events a year.
    For the past few years, Cronin and Alan A. Watson of the University of Leeds have been spearheading an initiative to gather an even larger sample of ultrahigh-energy cosmic rays. This development is named the Auger Project, after Pierre Auger, the French scientist who first investigated the phenomenon of correlated showers of particles from cosmic rays. The plan is to provide detectors with areas of 9,000 square kilometers that are capable of measuring hundreds of high-energy events a year. A detector field would consist of many stations on a 1.5-kilometer grid; a single event might trigger dozens of stations.
    An Auger Project design workshop held at the Fermi National Accelerator Laboratory in 1995 has shown how modern off-the-shelf technology such as solar cells, cellular telephones and Global Positioning System receivers can make such a system far easier to construct. A detector the size of Rhode Island could be built for about $50 million. To cover the entire sky, two such detectors are planned, one each for the Northern and Southern hemispheres.

    As researchers confront the problem of building and operating such gigantic detector networks, the fundamental question remains: Can nature produce even more energetic particles than those we have seen? Could there be still higher-energy cosmic rays, or are we already beginning to detect the highest-energy particles our universe can create?


    Further Reading

    Introduction to Ultrahigh Energy Cosmic Ray Physics. Pierre Sokolsky. Addison-Wesley, 1988.
    Cosmic Rays and Particle Physics. Thomas K. Gaisser. Cambridge University Press, 1990.
    High Energy Astrophysics, Vol. 1. Second edition. Malcolm S. Longair. Cambridge University Press, 1992.
    Cosmic Ray Observations below 1014 eV. Simon Swordy in Proceedings of the XXIII International Cosmic Ray Conference. Edited by D. A. Leahy, R. B. Hicks and D. Venkatesan. World Scientific, 1994.



    The Authors

    JAMES W. CRONIN, THOMAS K. GAISSER and SIMON P. SWORDY work on both the theoretical questions of how cosmic rays are created and the practical problems inherent in detecting and analyzing them. Cronin, a professor of physics at the University of Chicago since 1971, earned his master's degree from the university in 1953 and his doctorate in 1955. In 1980 he shared the Nobel Prize with Val L. Fitch for work on symmetry violations in the decay of mesons. Gaisser, a professor of physics at the University of Delaware, has concentrated on the interpretation of atmospheric cosmic-ray cascades; he earned his doctorate from Brown University in 1967. In 1995 Gaisser spent two months in Antarctica setting up cosmic-ray detectors. Swordy, an associate professor at Chicago, has been active in cosmic-ray measurement since 1976. He earned his Ph.D. from the University of Bristol in 1979.




    2.4 in Quark-Lepton Unification in XL-Boson Class HE(64)
    SeW.G --- S.EW.G


    higgs1. higgs2.



    2.5 The Continuous Inflaton in 10D/4D DeSitter Spacetime


    In the early radiation dominated cosmology; the quintessence was positive and the matter energy dominated the intrinsic Milgröm deceleration from the Instanton n=nps to n=0.18023 (about 3.04 Billion years) when the quintessence vanished and including a Recombination epoch when the hitherto opaque universe became transparent in the formation of the first hydrogen atoms from the quark-lepton plasma transmuted from the X-L Boson string class HO(32) of the Inflaton epoch preceding the Quantum Big Bang aka the Instanton.

    From the modular membrane duality for wormhole radius rps = λps/2π, the critical modulated Schwarzschild radius rss = 2πλss = 2πx1022 m* for λps = 1/λss
    and for an applied scalefactor a = n/[n+1] = λss/RH = {1-1/[n+1]}

    for a n=Hot coordinate nrecombination = 6.259485x10-5 or about 6.259485x10-5(16.88 Gy) = 1.056601 Million years
    attenuated by exp{-hf/kT} = e-1 = 0.367879 to a characteristic cosmological time coordinate of 0.36788x1.056601 = 388,702 years after the Instanton nps.

    The attenuation of the recombination coordinate then gives the cosmic temperature background for this epoch in the coordinate interval for the curvature radius
    R(n=2.302736x10-5) = 3.67894x1021 m* to R(n=6.259485x10-5) = 1022 m*.
    This radial displacement scale represents the size of a typical major galaxy in the cosmology; a galactic structure, which became potentialised in the Schwarzschild matter evolution and its manifestation in the ylemic prototypical first generation magnetar-neutron stars, whose emergence was solely dependent on the experienced cosmic temperature background and not on their mass distributions.


    The temperature evolution of the Instanton can be written as a function of the luminosity L(n,T) with R(n)=RH(n/[n+1]) as the radius of the luminating surface
    L(nps,T(nps) = 6π2λps2.σ.Tnps4 = 2.6711043034x1096 Watts*, where σ = Stefan's Constant = 2π5k4/15h3c2 and as a product of the defined 'master constants' k, h, c2, π and 'e'.

    L(n,T) = 3HoMo.c2/550n and for Temperature T(nps) ----------- T(nps) = 2.93515511x1036 Kelvin*.

    T(n)4 = HoMoc2/(2π2σRH2[550n3/[n+1]2]) for
    T(n)4 = {[n+1]2/n3}HoMoc2/(2π2σRH2[550]) = 18.1995{[n+1]2/n3} (K4/V)*
    for a temperature interval in using the recombination epoch coordinates T(n1=6.2302736x10-5) = 2945.42 K* to T(n2=6.259485x10-5) = 2935.11 K*


    This manifests as a 'false vacuum' and as a temperature gradient, as a causation of the Big Bang Instanton on physical grounds.
    The metaphysical ground is the symmetry breaking from the source parity violation described in the birth and necessity of the Graviton to resymmetrize the UFoQR.

    T(nps) of the singularity is 0.0389 or 3.89% of the pre-singularity.

    So the POTENTIAL Temperature manifests as 3.89% in the KINETIC Temperature' which doubles in the Virial Theorem to 7.78% as 2KE + PE = 0:
    TEMPERATURE/T(nps)=7.544808988..x1037/2.93515511x1036=25.705=1/0.03890...


    PlanckRad.

    Applying the actual VPE at the Instanton to this temperature gradient:

    ρVPE/rEMR = {4πEpsps3}/{8π5Eps4/15h3c3} = 15/2π4 = 0.07599486.. = 1/12.9878.. indicating the proportionality EVPE/EEMR = 2Tps/Tpotential at the Instanton from the Inflaton as a original form of the virial theorem, staing the Kinetic Energy of the Instanton and the QBB Lambda to be twice the Potential Energy of the de Broglie wave matter Inflaton, then manifesting as the Mo/2MHubble = rHyper/2RHubble Schwarzschild mass cosmo-evolution.

    Now reducing the timeinstanton tps=nps/Ho of 3.33x10-31 seconds by the Temperature Gradient in the Luminosity Function gives you the scalar Higgs Potential Maximum at a pre-singularity time of tHiggsPE = tps.T(nps)/TEMPERATURE=1.297x10-32 seconds.

    This then extrapolates the Big Bang singularity backwards in Time to harmonise the equations and to establish the 'driving force of the vacuum' as potential scalar Higgs Temperature Field.
    All the further evolvement of the universe so becomes a function of Temperature and not of mass.
    The next big phasetransition is the attunement of the BOSONIC UNIFICATION, namely the 'singularity' temperature Tps=1.41x1020 K with the Luminosity function.
    This occurs at a normal time of 1.9 nanoseconds into the cosmology.

    It is then that the universe as a unity has this temperature and so allows BOSONIC differentiation between particles. The INDIVIDUATED PHOTON of the mass was born then and not before, as the entire universe was a PHOTON as a macroquantised superstring up to then.
    The size of the universe at that time was that of being 1.14 metres across.
    Next came the electroweak symmetry breaking at 1/365 seconds and at a temperature of so 1015 Kelvin* and so it continued.

    The lower dimensional lightpath x=ct in lightspeed invariance c=lf so becomes modular dualised in the higher dimensional lightpath of the tachyonic de Broglie Inflaton-Instanton Vdebroglie=c/nps of the Inflaton.

    decepar.

    {(2-n)(n+1)}3/n3 = VdS'/VdS ......(4.36038 for npresent) in the first completing Hubble cycle
    n3/(2-n)3 =VAdS/VdS' ................. (2.22379 for npresent) in the first completing Hubble cycle
    (n+1)3 = VAdS/VdS .....................(9.69657 for npresent) in the first completing Hubble cycle

    ρcritical = 3Ho2/8πGo {Sphere} and Ho2/4π2Go {Hypersphere-Torus in factor 3π/2} (constant for all n per Hubble cycle)
    ρcritical = 3.78782x10-27 [kg/m3]* and 8.038003x10-28 [kg/m3]*


    ρdSVdS = rdS'VdS' = rAdSVAdS = rcriticalVHubble = MHubble = c2RH/2Go = 6.47061227x1052 kg*
     
    Last edited: Feb 16, 2018
  6. admin

    admin Well-Known Member Staff Member

    Messages:
    3,158
    3. The Instanton

    3.1 Bosonic Unification
    S.EW.G --- S.E.W.G

    The following derivations lead to a simplified string formalism as boundary- and initial conditions in a de Sitter cosmology encompassing the classical Minkowski-Friedmann spacetimes holographically and fractally in the Schwarzschild metrics.


    The magnetic field intensity B is classically described in the Biot-Savart Law:
    B=μoqv/4πr2oi/4πr=μoqω/4πr=μoNef/2r
    for a charge count q=Ne; angular velocity ω=v/r=2πf; current i=dq/dt and the current element i.dl=dq.(dl/dt)=vdq.

    The Maxwell constant then can be written as an (approximating) finestructure:
    μoεo =1/c2=(120π/c)(1/120πc) to crystallise the 'free space impedance' Zo=√(μoo)=120π~377 Ohm (Ω).

    This vacuum resistance Zo so defines a 'Unified Action Law' in a coupling of the electric permittivity component (εo) of inertial mass and the magnetic permeability component (μo) of gravitational mass in the Equivalence Principle of General Relativity.
    A unified selfstate of the preinertial (string- or brane) cosmology so is obtained from the finestructures for the electric- and gravitational interactions coupling a so defined electropolic mass to magnetopolic mass respectively.

    The Planck-Mass is given from Unity 1=2πGmP2/hc and the Planck-Charge derives from Alpha=2πke2/hc and where k=1/4πεo in the electromagnetic finestructure describing the probability interaction between matter and light (as about 1/137).

    The important aspect of alpha relates to the inertia coupling of Planck-Charge to Planck-Mass as all inertial masses are associated with Coulombic charges as inertial electropoles; whilst the stringed form of the Planck-Mass remains massless as gravitational mass. It is the acceleration of electropoles coupled to inertial mass, which produces electromagnetic radiation (EMR); whilst the analogy of accelerating magnetopoles coupled to gravitational mass and emitting electromagnetic monopolic radiation (EMMR) remains hitherto undefined in the standard models of both cosmology and particle physics.

    But the coupling between electropoles and magnetopoles occurs as dimensional intersection, say between a flat Minkowskian spacetime in 4D and a curved de Sitter spacetime in 5D (and which becomes topologically extended in 6-dimensional Calabi-Yau tori and 7-dimensional Joyce manifolds in M-Theory).

    The formal coupling results in the 'bounce' of the Planck-Length in the pre-Big Bang scenario, and which manifests in the de Broglie inflaton-instanton.

    The Planck-Length LP=√(hG/2πc3) 'oscillates' in its Planck-Energy mP=h/λPc=h/2πcLP to give √Alpha).LP=e/c2 in the coupling of 'Stoney units' suppressing Planck's constant 'h' to the 'Planck units' suppressing charge quantum 'e'.

    Subsequently, the Planck-Length is 'displaced' in a factor of about 11.7=1/√Alpha=√(h/60π)/e and using the Maxwellian finestructures and the unity condition kG=1 for a dimensionless string coupling Go=4πεo, describing the 'Action Law' for the Vacuum Impedance as Action=Charge2, say via dimensional analysis:

    Zo=√([Js2/C2m]/[C2/Jm])=[Js]/[C2]=[Action/Charge2] in Ohms [Ω=V/I=Js/C2] and proportional to [h/e2] as the 'higher dimensional source' for the manifesting superconductivity of the lower dimensions in the Quantum Hall Effect (~e2/h), the conductance quantum (2e2/h) and the Josephson frequencies (~2e/h) in Ohms [Ω].

    This derivation so indicates an electromagnetic cosmology based on string parameters as preceding the introduction of inertial mass (in the quantum Big Bang) and defines an intrinsic curvature within the higher dimensional (de Sitter) universe based on gravitational mass equivalents and their superconductive monopolic current flows.

    A massless, but monopolically electromagnetic de Sitter universe would exhibit intrinsic curvature in gravitational mass equivalence in its property of closure under an encompassing static Schwarzschild metric and a Gravitational String-Constant Go=1/k=1/30c (as given in the Maxwellian finestructures in the string space).

    In other words, the Big Bang manifested inertial parameters and the matter content for a subsequent cosmoevolution in the transformation of gravitational 'curvature energy', here called gravita as precursor for inertia into inertial mass seedlings; both however describable in Black Hole physics and the Schwarzschild metrics.

    The Gravitational Finestructure so derives in replacing the Planck-Mass mP by a protonucleonic mass:

    mc=√(hc/2πGo).f(alpha)= f(Alpha).mP and where f(Alpha)=Alpha9.
    The Gravitational finestructure, here named Omega, is further described in a fivefolded supersymmetry of the string hierarchies, the latter as indicated in the following below in excerpt.

    This pentagonal supersymmetry can be expressed in a number of ways, say in a one-to-one mapping of the Alpha finestructure constant as invariant X from the Euler Identity:

    X+Y=XY= -1=i2=exp(iπ).

    One can write a Unification Polynomial: (1-X)(X)(1+X)(2+X)=1 or X4+2X3-X2-2X+1=0
    to find the coupling ratios: f(S)¦f(E)¦f(W)¦f(G)=#¦#3¦#18¦#54 from the proportionality
    #¦#3¦{[(#3)2]}3¦({[(#3)2]}3)3=Cuberoot(Alpha):Alpha:Cuberoot(Omega):Omega.

    The Unification polynomial then sets the ratios in the inversion properties under modular duality:

    (1)[Strong short]¦(X)[Electromagnetic long]¦(X2)[Weak short]¦(X3)[Gravitational long]
    as 1¦X¦X2¦X3 = (1-X)¦(X)¦(1+X)¦(2+X).

    Unity 1 maps as (1-X) transforming as f(S) in the equality (1-X)=X2; X maps as invariant of f(E) in the equality (X)=(X); X2 maps as (1+X) transforming as f(W) in the equality (1+X)=1/X; and X3 maps as (2+X) transforming as f(G) in the equality (2+X)=1/X2=1/(1-X).

    The mathematical pentagonal supersymmetry from the above then indicates the physicalised T-duality of M-theory in the principle of mirror-symmetry and which manifests in the reflection properties of the heterotic string classes HO(32) and HE(64), described further in the following.

    Defining f(S)=#=1/f(G) and f(E)=#2.f(S) then describes a symmetry breaking between the 'strong S' f(S) interaction and the 'electromagnetic E' f(E) interaction under the unification couplings.
    This couples under modular duality to f(S).f(G)=1=#55 in a factor #-53=f(S)/f(G)={f(S)}2 of the 'broken' symmetry between the longrange- and the shortrange interactions.

    SEWG=1=Strong-Electromagnetic-Weak-Gravitational as the unified supersymmetric identity then decouples in the manifestation of string-classes in the de Broglie 'matter wave' epoch termed inflation and preceding the Big Bang, the latter manifesting at Weyl-Time as a string-transformed Planck-Time as the heterotic HE(64) class.

    As SEWG indicates the Planck-String (class I, which is both openended and closed), the first transformation becomes the suppression of the nuclear interactions sEwG and describing the selfdual monopole (stringclass IIB, which is loop-closed in Dirichlet brane attachement across dimensions say Kaluza-Klein R5 to Minkowski R4 or Membrane-Space R11 to String Space R10).

    The monopole class so 'unifies' E with G via the gravitational finestructure assuming not a Weylian fermionic nucleon, but the bosonic monopole from the kGo=1 initial-boundary condition GmM2= ke2 for mM=ke=30[ec]=mP√Alpha.

    The Planck-Monopole coupling so becomes mP/mM=mP/30[ec]=1/√Alpha
    with f(S)=f(E)/#2 modulating f(G)=#2/f(E)=1/# ↔ f(G){f(S)/f(G)}=# in the symmetry breaking f(S)/f(G)=1/#53 between short (nuclear asymptotic) and long (inverse square).

    The shortrange coupling becomes f(S)/f(W)=#/#18=1/#17=Cuberoot(Alpha)/Alpha6
    and the longrange coupling is Alpha/Omega=1/Alpha17=#3/#54=1/#51=1/(#17)3.

    The strong nuclear interaction coupling parameter so becomes about 0.2 as the cuberoot of alpha and as measured in the standard model of particle physics.

    The monopole quasimass [ec] describes a monopolic sourcecurrent ef, manifesting for a displacement λ=c/f. This is of course the GUT unification energy of the Dirac Monopole at precisely [c3] eV or 2.7x1016 GeV and the upper limit for the Cosmic Ray spectra as the physical manifestation for the string classes: {I, IIB, HO(32), IIA and HE(64) in order of modular duality transmutation}.

    The transformation of the Monopole string into the XL-Boson string decouples Gravity from sEwG in sEw.G in the heterotic superstring class HO(32). As this heterotic class is modular dual to the other heterotic class HE(64), it is here, that the protonucleon mass is defined in the modular duality of the heterosis in: Omega=Alpha18=2πGomc2/hc=(mc/mP)2.

    The HO(32) string bifurcates into a quarkian X-part and a leptonic L-part, so rendering the bosonic scalar spin as fermionic halfspin in the continuation of the 'breaking' of the supersymmetry of the Planckian unification. Its heterosis with the Weyl-string then decouples the strong interaction at Weyl-Time for a Weyl-Mass mW, meaning at the timeinstanton of the end of inflation or the Big Bang in sEw.G becoming s.Ew.G.

    The X-Boson then transforms into a fermionic protonucleon triquark-component (of energy ~ 10-27 kg or 560 MeV) and the L-Boson transforms into the protomuon (of energy about 111 MeV).

    The last 'electroweak' decoupling then occurs at the Fermi-Expectation Energy about 1/365 seconds after the Big Bang at a temperature of about 3.4x1015 K and at a 'Higgs Boson' energy of about 298 GeV.

    A Bosonic decoupling preceeded the electroweak decoupling about 2 nanoseconds into the cosmogenesis at the Weyl-temperature of so TWeyl=Tmax=EWeyl/k=1.4x1020 K as the maximum Black Hole temperature maximised in the Hawking MT modulus and the Hawking-Gibbons formulation: McriticalTmin=½MPlanckTPlanck=(hc/2πGo)(c2/2k)=hc3/4πkGo for Tmin=1.4x10-29 K and Boltzmann constant k.

    The Hawking Radiation formula results in the scaling of the Hawking MT modulus by the factor of the 'Unified Field' spanning a displacement scale of 8p radians or 1440° in the displacement of 4lps.

    The XL-Boson mass is given in the quark-component: mX=#3mW/[ec]=Alpha.mW/mP=#3{mW/mP}~1.9x1015 GeV; and the lepton-component: mL=Omega.[ec]/#2=#52[ec/mW] ~ 111 MeV.

    A reformulation of the rotational dynamics associated with the monopolic naturally superconductive currentflow and the fractalisation of the static Schwarzschild solution follows. in a reinterpretation of the Biot-Savart Law.

    All inertial objects are massless as 'Strominger branes' or extremal boundary Black Hole equivalents and as such obey the static and basic Schwarzschild metric as gravita template for inertia.

    This also crystallises the Sarkar Black Hole boundary as the 100Mpc limit (RSarkar=(Mo/Mcritical.RHubble)=0.028.RHubble~237 Million lightyears) for the cosmological principle, describing large scale homogeneity and isotropy, in the supercluster scale as the direct 'descendants' of Daughter Black Holes from the Universal Mother Black Hole describing the Hubble Horizon as the de Sitter envelope for the Friedmann cosmology (see linked website references on de Sitter cosmology) for the oscillatory universe bounded in the Hubble nodes as a standing waveform.

    The Biot-Savart Law: B=μoqv/4πr2oi/4πr=μoNef/2r=μoNeω/4πr for angular velocity ω=v/r transforms into B=constant(e/c3)gxω

    in using acentripetal=v2/r=rω2 for g=GM/r2=(2GM/c2)(c2/2r2)=(RSc2/2R2) for a Schwarzschild solution RS=2GM/c2.

    B=constant(eω/rc)(v/c)2oNeω/4πr yields constant=μoNc/4π=(120πN/4π)=30N with e=mM/30c for
    30N(eω/c3)(GM/R2)=30N(mM/30c)ω(2GM/c2)/(2cR2)=NmM(ω/2c2R)(RS/R)= {M}ω/2c2R.

    Subsequently, B=Mw/2c2R = NmM(RS/R){ω/2c2R} to give a manifesting mass M finestructured in
    M=NmM(RS/R) for N=2n in the superconductive 'Cooper-Pairings' for a charge count q=Ne=2ne.

    But any mass M has a Schwarzschild radius RS for N=(M/mM){R/RS}=(M/mM){Rc2/2GM}={Rc2/2GmM}={R/RM} for a monopolic Schwarzschild radius RM=2GmM/c2=2G(30ec)/c2=60ec/30c3=2e/c2=2LP√Alpha=2OLP.

    Any mass M is quantised in the Monopole mass mM=mP√Alpha in its Schwarzschild metric and where the characterising monopolic Schwarzschild radius represents the minimum metric displacement scale as the Oscillation of the Planck-Length in the form 2LP√Alpha~LP/5.85.

    This relates directly to the manifestation of the magnetopole in the lower dimensions, say in Minkowski spacetime in the coupling of inertia to Coulombic charges, that is the electropole and resulting in the creation of the mass-associated electromagnetic fields bounded in the c-invariance.
    From the Planck-Length Oscillation or 'LP-bounce': OLP=LP√Alpha=e/c2 in the higher (collapsed or enfolded) string dimensions, the electropole e=OLP.c2 maps the magnetopole e*=2Re.c2 as 'inverse source energy' EWeyl=hfWeyl and as function of the classical electron radius Re =ke2/mec2=RCompton.Alpha= RBohr1.Alpha2=Alpha3/4πRRydberg= 1010{2πRW/360}={e*/2e}.OLP.

    The resulting reflection-mirror space of the M-Membrane space (in 11D) so manifests the 'higher D' magnetocharge 'e*' AS INERTIAL MASS in the monopolic current [ec], that is the electropolic Coulomb charge 'e'.
    This M-space becomes then mathematically formulated in the gauge symmetry of the algebraic Lie group E8 and which generates the inertial parameters of the classical Big Bang in the Weylian limits and as the final Planck-String transformation.

    The string-parametric Biot-Savart law then relates the angular momentum of any inertial object of mass M with angular velocity ω in selfinducing a magnetic flux intensity given by B=Mω/2Rc2 and where the magnetic flux relates inversely to a displacement R from the center of rotation and as a leading term approximation for applicable perturbation series.

    This descriptor of a string based cosmology so relates the inherent pentagonal supersymmetry in the cosmogenesis to the definition of the Euler identity in its finestructure X+Y=XY=-1, and a resulting quadratic with roots the Golden Mean and the Golden Ratio of the ancient omniscience of harmonics, inclusive of the five Platonic solids mapping the five superstring classes. Foundations and applications of superstring theory are also indicated and serve as reference for the above.





    3.2 Baryogenesis without Antimatter

    baryogenesis.

    Matter-Antimatter Asymmetry: CERN Experiments On Particles Containing Charm Quark Fail To Detect CP Violation

    By Avaneesh Pandey @avaneeshp88 On 09/29/16 AT 7:12 AM

    cern-lhc.PNG
    A view of the Large Hadron Collider (LHC) at CERN. Photo: CERN

    Why is there something rather than nothing? This is a question that has, for the longest time, perplexed physicists.
    If our current understanding of the universe is correct, it should not even exist. The very fact that planets, stars and galaxies exist undercuts one of the most fundamental premises of particle physics — that the Big Bang, which created our universe 13.8 billion years ago, created equal amounts of matter and antimatter.
    If this really happened, why, given that matter and antimatter particles annihilate each other when they collide, does anything exist at all? Why do you and I exist when the laws of physics, as we know them, seem to dictate that the cosmos should be nothing but a wasteland strewn with leftover energy?
    Obviously, as attested by the fact that we exist, there is a fundamental difference between matter and antimatter. Either significantly more matter was created by the Big Bang, or there is a fundamental, as-of-yet-undiscovered asymmetry between matter particles and their antimatter counterparts — one that would have given the former an edge over the latter in the race for survival.

    The quest to discover this asymmetry is a goal that has witnessed the involvement of several particle physicists from across the world, including researchers at the European Organization for Nuclear Research (CERN) — the institution that houses the world’s most powerful particle collider.
    On Wednesday, researchers associated with the LHCb experiment at the Large Hadron Collider announced that they had made the most precise measurement of Charge-Parity (CP) violation among particles containing a charm quark.
    Quarks, the fundamental particles that make up protons and neutrons, come in six different “flavors” — up, down, strange, top, bottom and charm. Each quark has an antimatter equivalent known as antiquark. Both protons and neutrons — contained within the nucleus of an atom — are made up of three quarks bound together.
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    The Standard Model of particle physics, which describes how three of the four known fundamental forces work, has a central tenet — charge-parity symmetry, which posits that the laws of physics remain unchanged even if a particle is replaced with its antiparticle, which has the opposite charge, and if its spatial coordinates are inverted.
    If a significant violation of CP symmetry is detected, it would not only hint at the existence of physics beyond the Standard Model, it would also help us understand why the universe is completely devoid of antimatter.

    So far, however, the extent of CP violation detected among elementary particles is not significant enough to explain the observed matter-antimatter asymmetry — something that was further confirmed by the precise measurements carried out by LHCb researchers.
    “The LHCb collaboration made a precise comparison between the decay lifetime of a particle called a D0meson (formed by a charm quark and an up antiquark) and its anti-matter counterpart D0 (formed by an charm antiquark and up quark), when decaying either to a pair of pions or a pair of kaons. Any difference in these lifetimes would provide strong evidence that an additional source of CP violation is at work,” CERN said in the statement. “The latest results indicate that the lifetimes of the D0 and D0 particles, measured using their decays to pions or kaons, are still consistent, thereby demonstrating that any CP violation effect that is present must indeed be at a tiny level.”

    baryogenesis.

    There is no CP-violation in any quark whose constituents are up-quarks and anti-up quarks, as is the case for the charm quarks c-uu[bar]u and c[bar]=u[bar]uu[bar], as the CP violation requires Inner-Ring (down-anti-down) or Outer-Ring (strange-anti-strange) interaction.

    ufoqrpdf.

    The Top-Super Diquark Resonance of CERN - December 15th, 2015

    As can be calculated from the table entries below; a Top-Super Diquark Resonance is predicted as a (ds)bar(ss)=(ds)barS or a (ds)(ss)bar=(ds)Sbar diquark complex averaged at (182.783+596.907)GeV=779.690 GeV.
    atlas_cms_diphoton_2015--31707-.31710.

    In the diquark triplet {dd; ds; ss}={Dainty; Top; Super} a Super-Superbar resonance at 1.1938 TeV can also be inferred with the Super-Dainty resonance at 652.9 GeV and the Top-Dainty resonance at 238.747 GeV 'suppressed' by the Higgs Boson summation as indicated below. Supersymmetric partners become unnecessary in the Standard Model, extended into the diquark hierarchies.
    Ten DIQUARK quark-mass-levels crystallise, including a VPE-level for the K-IR transition and a VPE-level for the IR-OR transition:

    VPE-Level [K-IR] is (26.4959-29.9663 MeV*) for K-Mean: (14.11554 MeV*); (2.8181-3.1872 MeV*) for IROR for L-Mean: 1.501325 MeV*;
    VPE-Level [IR-OR] is (86.5383-97.8729 MeV*) for K-Mean: (46.1028 MeV*); (9.2042-10.410 MeV*) for IROR; for L-Mean: 4.90355 MeV*
    UP/DOWN-Level is (282.5655-319.619 MeV*) for K-Mean: (150.5767 MeV*); (30.062-33.999 MeV*) for IROR;
    STRANGE-Level is (923.1410-1,044.05 MeV*) for K-Mean: (491.7990 MeV*); (98.185-111.05 MeV*) for IROR;
    CHARM-Level is (3,015.08-3,409.98 MeV*) for K-Mean: (1,606.266 MeV*); (320.68-362.69 MeV*) for IROR;
    BEAUTY-Level is (9,847.55-11,137.34 MeV*) for K-Mean: (5,246.223 MeV*); (1,047.4-1,184.6 MeV*) for IROR;
    MAGIC-Level is (32,163.1-36,375.7 MeV*) for K-Mean: (17,134.71 MeV*); (3,420.9-3,868.9 MeV*) for IROR;
    DAINTY-Level is (105,048-118,807 MeV*) for K-Mean: (55,963.7 MeV*); (11,173-12,636 MeV*) for IROR;
    TRUTH-Level is (343,098-388,036 MeV*) for K-Mean: (182,783.3 MeV*); (36,492-41,271 MeV*) for IROR;
    SUPER-Level is (1,120,592-1,267,366 MeV*) for K-Mean: (596,906.8 MeV*); (119,186-134,797 MeV*) for IROR.

    The K-Means define individual materialising families of elementary particles;

    the (UP/DOWN-Mean) sets the (PION-FAMILY: πo, π+, π-);
    the (STRANGE-Mean) specifies the (KAON-FAMILY: Ko, K+, K-);
    the (CHARM-Mean) defines the (J/PSI=J/Ψ-Charmonium-FAMILY);
    the (BEAUTY-Mean) sets the (UPSILON=Υ-Bottonium-FAMILY);
    the (MAGIC-Mean) specifies the (EPSILON=Ε-FAMILY);
    the (DAINTY-Mean) bases the (OMICRON-Ο-FAMILY);
    the (TRUTH-Mean) sets the (KOPPA=Κ-Topomium-FAMILY) and
    the (SUPER-Mean) defines the final quark state in the (HIGGS/CHI=H/Χ-FAMILY).

    The VPE-Means are indicators for average effective quarkmasses found in particular interactions.
    Kernel-K-mixing of the wavefunctions gives K(+)=60.218 MeV* and K(-)=31.987 MeV* and the IROR-Ring-Mixing gives (L(+)=6.405 MeV* and L(-)=3.402 MeV*) for a (L-K-Mean of 1.50133 MeV*) and a (L-IROR-Mean of 4.90355 MeV*); the Electropole ([e-]=0.52049 MeV* and 3x(0.17350 MeV* for e±/3) as the effective electronmass and as determined from the electronic radius and the magnetocharge in the UFoQR.

    The restmasses for the elementary particles can now be constructed, using the basic nucleonic restmass (mc=9.9247245x10-28 kg*=(√(OmegaxmP) for np as 1.71175286x10-27 kg* or 958.99 MeV* and setting
    (mc) as the basic maximum (UP/DOWN-K-mass=mass(KERNEL CORE)=3xmass(KKK)=3x319.6637 MeV*=958.991 MeV*);
    Subtracting the (Ring VPE 3xL(+)=19.215 MeV*, one gets the basic nucleonic K-state for the atomic nucleus (made from protons and neutrons) in: {m(n0;p+)=939.776 MeV*}.


    The HB discussed in the New Scientist post below is said of having been measured in the decay of W's, Z's and Tau Leptons, as well as the bottom- and top-quark systems described in the table and the text above.

    Now in the table I write about the KIR-OR transitions and such. The K means core for kernel and the IR means InnerRing and the OR mean OuterRing. The Rings are all to do with Leptons and the Kernels with Quarks.

    So the Tau-decay relates to 'Rings' which are charmed and strange and bottomised and topped, say. They are higher energy manifestations of the basic nucleons of the proton and the neutrons and basic mesons and hyperons.



    Is This the Beginning of the End of the Standard Model?

    Posted on December 16, 2015 | 15 Comments
    Was yesterday the day when a crack appeared in the Standard Model that will lead to its demise? Maybe. It was a very interesting day, that’s for sure. [Here’s yesterday’s article on the results as they appeared.]
    I find the following plot useful… it shows the results on photon pairs from ATLAS and CMS superposed for comparison. [I take only the central events from CMS because the events that have a photon in the endcap don’t show much (there are excesses and deficits in the interesting region) and because it makes the plot too cluttered; suffice it to say that the endcap photons show nothing unusual.] The challenge is that ATLAS uses a linear horizontal axis while CMS uses a logarithmic one, but in the interesting region of 600-800 GeV you can more or less line them up. Notice that CMS’s bins are narrower than ATLAS’s by a factor of 2.
    atlas_cms_diphoton_2015-.31707.
    The diphoton results from ATLAS (top) and CMS (bottom) arranged so that the 600, 700 and 800 GeV locations (blue vertical lines) line up almost perfectly. (The plots do not line up away from this region!) The data are the black dots (ignore the bottom section of CMS’s plot for now.) Notice that the obvious bumps in the two data sets appear in more or less the same place. The bump in ATLAS’s data is both higher (more statistically significant) and significantly wider.


    Both plots definitely show a bump. The two experiments have rather similar amounts of data, so we might have hoped for something more similar in the bumps, but the number of events in each bump is small and statistical flukes can play all sorts of tricks.
    Of course your eye can play tricks too. A bump of a low significance with a small number of events looks much more impressive on a logarithmic plot than a bump of equal significance with a larger number of events — so beware that bias, which makes the curves to the left of the bump appear smoother and more featureless than they actually are. [For instance, in the lower register of CMS’s plot, notice the bump around 350.]

    We’re in that interesting moment when all we can say is that there might be something real and new in this data, and we have to take it very seriously. We also have to take the statistical analyses of these bumps seriously, and they’re not as promising as these bumps look by eye. If I hadn’t seen the statistical significances that ATLAS and CMS quoted, I’d have been more optimistic.

    Also disappointing is that ATLAS’s new search is not very different from their Run 1 search of the same type, and only uses 3.2 inverse femtobarns of data, less than the 3.5 that they can use in a few other cases… and CMS uses 2.6 inverse femtobarns. So this makes ATLAS less sensitive and CMS more sensitive than I was originally estimating… and makes it even less clear why ATLAS would be more sensitive in Run 2 to this signal than they were in Run 1, given the small amount of Run 2 data. [One can check that if the events really have 750 GeV of energy and come from gluon collisions, the sensitivity of the Run 1 and Run 2 searches are comparable, so one should consider combining them, which would reduce the significance of the ATLAS excess. Not to combine them is to “cherry pick”.]

    By the way, we heard that the excess events do not look very different from the events seen on either side of the bump; they don’t, for instance, have much higher total energy. That means that a higher-energy process, one that produces a new particle at 750 GeV indirectly, can’t be a cause of big jump in the 13 TeV production rate relative to 8 TeV. So one can’t hide behind this possible explanation for why a putative signal is seen brightly in Run 2 and was barely seen, if at all, in Run 1.
    Of course the number of events is small and so these oddities could just be due to statistical flukes doing funny things with a real signal. The question is whether it could just be statistical flukes doing funny things with the known background, which also has a small number of events.
    And we should also, in tempering our enthusiasm, remember this plot: the diboson excess that so many were excited about this summer. Bumps often appear, and they usually go away. R.I.P.
    atlas_dibosonxs-.31708.
    The most dramatic of the excesses in the production of two W or Z bosons from Run 1 data, as seen in ATLAS work published earlier this year. That bump excited a lot of people. But it doesn’t appear to be supported by Run 2 data. A cautionary tale.

    Nevertheless, there’s nothing about this diphoton excess which makes it obvious that one should be pessimistic about it. It’s inconclusive: depending on the statistical questions you ask (whether you combine ATLAS and CMS Run 2, whether you try to combine ATLAS Run 1 and Run 2, whether you worry about whether the resonance is wide or narrow), you can draw positive or agnostic conclusions. It’s hard to draw entirely negative conclusions… and that’s a reason for optimism.

    Six months or so from now — or less, if we can use this excess as a clue to find something more convincing within the existing data — we’ll likely say “R.I.P.” again. Will we bury this little excess, or the Standard Model itself?

    http://profmattstrassler.com/2015/12/16/is-this-the-beginning-of-the-end-of-the-standard-model/

    Hints of Higgs Boson at 125 GeV Are Found:
    Congratulations to All the People at LHC!
    cover_issue_23_en_us--16765-.31709.


    Refined Higgs Rumours, Higgs Boson Live Blog: Analysis of the CERN Announcement, Has CERN Found the God Particle? A Calculation, Electron Spin Precession for the Time Fractional Pauli Equation, Plane Wave Solutions of Weakened Field Equations in a Plane Symmetric Space-time-II, Plane Wave Solutions of Field Equations of Israel and Trollope's Unified Field Theory in V5, If the LHC Particle Is Real, What Is One of the Other Possibilities than the Higgs Boson? What is Reality in a Holographic World? Searching for Earth’s Twin.

    Editor: Huping HU, Ph.D., J.D.; Editor-at-Large: Philip E. Gibbs, Ph.D.

    ISSN: 2153-8301

    Dear Huping!

    The Higgs Boson resonance, found by ATLAS and CMS is a diquark resonance.

    Excerpt:

    "Ok, now I'll print some excerpt for the more technically inclined reader regarding the Higgs Boson and its 'make-up', but highlight the important relevant bit (wrt to this discovery of a 160 GeV Higgs Boson energy, and incorporating the lower energy between 92 GeV and to the upper dainty level at 130 GeV as part of the diquark triplet of the associated topomium energy level) at the end.

    In particular, as the bottomium doublet minimum is at 5,246.223 MeV* and the topomium triplet minimum is at 55,963.7 MeV* in terms of their characteristic Kernel-Means, their doubled sum indicates a particle-decay excess at the recently publisized ~125 GeV energy level in 2x(5.2462+55.9637) GeV* = 122.420 GeV* (or 122.119 GeV SI).
    These are the two means from ATLAS {116-130 GeV as 123 GeV} and CMS {115-127 GeV as 121 GeV} respectively.

    http://press.web.cern.ch/press/PressReleases/Releases2011/PR25.11E.html

    Then extending the minimum energy levels, like as in the case to calculate the charged weakon gauge field agent energy in the charm and the VPE perturbations as per the table given, specifies the 125 GeV energy level in the Perturbation Integral/Summation:

    2x{55.964+5.246+1.606+0.492+0.151+0.046+0.014} GeV* = 127.02 GeV*, which become about 126.73 GeV SI as an UPPER LIMIT for this 'Higgs Boson' at the Dainty quark resonance level from the UFoQR (Unified Field of Quantum relativity).
    Using the 3 Diquark energy levels U,D and S yield 2x{55.964+5.246+1.606} GeV* = 125.63 GeV* and 125.32 GeV SI.""




    This newest data/discovery about the Higgs Boson aka the 'God-Particle' states, that there seems to be a 'resonance-blip' at an energy of about 160 GeV and as just one of say 5 Higgs Bosons for a 'minimal supersymmetry'.
    One, the lowest form of the Higgs Boson is said to be about 110 GeV in the Standard Model. There is also a convergence of the HB to an energy level of so 120 GeV from some other models.
    Now the whole thing , according to Quantum Relativity' about the Higgs Boson, is that IT IS NOT a particular particle, but relates to ALL particles in its 'scalar nature' as a restmass inducer.

    I have discussed the Higgs Boson many times before; but would like here to show in a very simple analysis that the Higgs Boson MUST show a blip at the 160 GeV mark and due to its nature as a 'polarity' neutraliser (a scalar particle has no charge and no spin, but can be made up of two opposite electric charges and say two opposing chiralities of spin orientations.)

    Without worrying about details, first consider the following table which contains all the elementary particles of the standard model of particle physics. The details are found in the Planck-String transformations discussed elesewhere.

    The X-Boson's mass is: ([Alpha α]xmps/[ec]) modulated in (SNI/EMI={Alpha}/[Alpha]), the intrisic unified Interaction-Strength and as the L-Boson's mass in: ([Omega]x([ec])/(mpsx
    (α2).

    Ten DIQUARK quark-mass-levels crystallise, including a VPE-level for the K-IR transition and a VPE-level for the IR-OR transition:

    VPE-Level [K-IR] is (26.4959-29.9663 MeV*) for K-Mean: (14.11554 MeV*); (2.8181-3.1872 MeV*) for IROR for L-Mean: 1.501325 MeV*;
    VPE-Level [IR-OR] is (86.5383-97.8729 MeV*) for K-Mean: (46.1028 MeV*); (9.2042-10.410 MeV*) for IROR; for L-Mean: 4.90355 MeV*
    UP/DOWN-Level is (282.5655-319.619 MeV*) for K-Mean: (150.5767 MeV*); (30.062-33.999 MeV*) for IROR;
    STRANGE-Level is (923.1410-1,044.05 MeV*) for K-Mean: (491.7990 MeV*); (98.185-111.05 MeV*) for IROR;
    CHARM-Level is (3,015.08-3,409.98 MeV*) for K-Mean: (1,606.266 MeV*); (320.68-362.69 MeV*) for IROR;
    BEAUTY-Level is (9,847.55-11,137.34 MeV*) for K-Mean: (5,246.223 MeV*); (1,047.4-1,184.6 MeV*) for IROR;
    MAGIC-Level is (32,163.1-36,375.7 MeV*) for K-Mean: (17,134.71 MeV*); (3,420.9-3,868.9 MeV*) for IROR;
    DAINTY-Level is (105,048-118,807 MeV*) for K-Mean: (55,963.7 MeV*); (11,173-12,636 MeV*) for IROR;
    TRUTH-Level is (343,098-388,036 MeV*) for K-Mean: (182,783.3 MeV*); (36,492-41,271 MeV*) for IROR;
    SUPER-Level is (1,120,592-1,267,366 MeV*) for K-Mean: (596,906.8 MeV*); (119,186-134,797 MeV*) for IROR.

    The K-Means define individual materialising families of elementary particles;

    the (UP/DOWN-Mean) sets the (PION-FAMILY: πo, π+, π-);
    the (STRANGE-Mean) specifies the (KAON-FAMILY: Ko, K+, K-);
    the (CHARM-Mean) defines the (J/PSI=J/Ψ-Charmonium-FAMILY);
    the (BEAUTY-Mean) sets the (UPSILON=Υ-Bottonium-FAMILY);
    the (MAGIC-Mean) specifies the (EPSILON=Ε-FAMILY);
    the (DAINTY-Mean) bases the (OMICRON-Ο-FAMILY);
    the (TRUTH-Mean) sets the (KOPPA=Κ-Topomium-FAMILY) and
    the (SUPER-Mean) defines the final quark state in the (HIGGS/CHI=H/Χ-FAMILY).

    The VPE-Means are indicators for average effective quarkmasses found in particular interactions.
    Kernel-K-mixing of the wavefunctions gives K(+)=60.218 MeV* and K(-)=31.987 MeV* and the IROR-Ring-Mixing gives (L(+)=6.405 MeV* and L(-)=3.402 MeV*) for a (L-K-Mean of 1.50133 MeV*) and a (L-IROR-Mean of 4.90355 MeV*); the Electropole ([e-]=0.52049 MeV* and 3x(0.17350 MeV* for e±/3) as the effective electronmass and as determined from the electronic radius and the magnetocharge in the UFoQR.

    The restmasses for the elementary particles can now be constructed, using the basic nucleonic restmass (mc=9.9247245x10-28 kg*=(√(OmegaxmP) for np as 1.71175286x10-27 kg* or 958.99 MeV* and setting
    (mc) as the basic maximum (UP/DOWN-K-mass=mass(KERNEL CORE)=3xmass(KKK)=3x319.6637 MeV*=958.991 MeV*);
    Subtracting the (Ring VPE 3xL(+)=19.215 MeV*, one gets the basic nucleonic K-state for the atomic nucleus (made from protons and neutrons) in: {m(n0;p+)=939.776 MeV*}.


    The HB discussed in the New Scientist post below is said of having been measured in the decay of W's, Z's and Tau Leptons, as well as the bottom- and top-quark systems described in the table and the text above.

    Now in the table I write about the KIR-OR transitions and such. The K means core for kernel and the IR means InnerRing and the OR mean OuterRing. The Rings are all to do with Leptons and the Kernels with Quarks.

    So the Tau-decay relates to 'Rings' which are charmed and strange and bottomised and topped, say. They are higher energy manifestations of the basic nucleons of the proton and the neutrons and basic mesons and hyperons.

    As I have shown, the energy resonances of the Z-boson (uncharged) represents an 'average' or statistical mean value of the 'Top-Quark' and the Upper-Limit for the Higgs Boson is a similar 'Super-Quark' 'average' and as the weak interaction unification energy.

    The hitherto postulated Higgs Boson mass of so 110 GeV is the Omicron-resonance, fully predicted from the table above (unique to Quantum Relativity).
    Now the most fundamental way to generate the Higgs Boson as a 'weak interaction' gauge is through the coupling of two equal mass, but oppositely charged W-bosons (of whom the Zo is the uncharged counterpart).

    We have seen, that the W-mass is a summation of all the other quark-masses as kernel-means from the strangeness upwards to the truth-quark level.
    So simply doubling the 80.593 GeV* and 80.395 GeV mass of the weak-interaction gauge boson must represent the basic form of the Higgs Boson and that is 161.186 GeV* or 160.790 GeV as a function of the electro-weak coupling.


    From Electro-Weak Unification parameters: {1eV = 1.0024656 eV*} with T(nEW=4.67x10-21) =3.40x1015 K*
    MW± = ΣKernel-Mean = mup-down+mstrange+mcharm+mmagic+mdainty+mbottom
    = 0.151+0.492+1.606+5.246+17.135+55.964 = 80.594 GeV*
    MZo = 91.39165 GeV* or 91.167 GeV
    M = 298.453 GeV* or 297.717 GeV
    √2.Fermi Constant G = √2.GF = √2{πα/(√2.MW2[1-MW2/MZ2])} = (1/Higgs-Vacuum-Expectation HVE)2 = 1.5873x10-5 GeV-2* for HVE=251.00 GeV* or 250.38 GeV

    As the Charmonium quark state is defined by the coupling of a double-up-diquark U=uu to an anti-up-quark as c=Uu(bar) and so as a quark molecule as the quark singlet state of 3 interacting quarks; whilst the diquark doublet of bottom-magic {b=[ud]bar and m=[us]bar} and the diquark triplet of dainty-top-super {D=[dd]bar and t=[ds]bar and S=[ss]bar} form double quarks; the Kernel-Mean of the Charmonium energy level is added to the HVE and the Difference-VPE levels for the K-IR - IR-OR transitions are subtracted for the quark-antiquark coupling.

    MW- + MW+ + MZo = 252.578 GeV* = HVE + mcharm - (mK(-) - mL(-)) = (251.00 + 1.6063 - [0.031987-0.003402]) = 252.578 GeV* or 251.957 GeV
    300.031 GeV* - M = mcharm - (mK(-) - mL(-)) = MW- + MW+ + MZo - HEV = 1.578 GeV*
    mcharm = MW- + MW+ + MZo + (mK(-) - mL(-)) - HEV = 1.6063 GeV* or 1.6023 GeV.


    Simplicity indeed and just the way Quantum Relativity describes the creation of the Higgs Boson from even more fundamental templates of the so called 'gauges'. The Higgs Boson is massless but consists of two classical electron rings and a massless doubled neutrino kernel, and then emerges in the magnetocharge induction AS mass carrying gauges.

    This massless neutrino kernel now crystallises our atomic solar system.


    Next we interpret this scalar (or sterile) Double-Higgs (anti)neutrino as a majoron and lose the distinction between antineutrino and neutrino eigenstates.

    We can only do this in the case of the Zo decay pattern, which engage the boson spin of the Zo as a superposition of two antineutrinos for the matter case and the superposition of two neutrinos in the antimatter case from first principles.

    So the Zo IS a Majorana particle, which merges the templates of two antineutrinos say and SPININDUCES the Higgs-Antineutrino.
    And where does this occur? It occurs at the Mesonic-Inner-Ring Boundary previously determined at the 2.776x10-18 meter marker.
    This marker so specifies the Zo Boson energy level explicitely as an upper boundary relative to the displacement scale set for the kernel at the wormhole radius rw=lw/2π and the classical electron radius as the limit for the nuclear interaction scale at 3 fermis in: RcomptonxAlpha.

    So the particle masses of the standard model in QED and QCD become Compton-Masses, which are HIGGS-MASSINDUCED at the Mesonic-Inner-Ring (MIR) marker at RMIR=2.776x10-18 meters.

    The Compton masses are directly obtained from E=hf=mc2=hc/λ and say as characteristic particle energies.
    At the Leptonic-Outer-Ring or LOR; λLOR=2πRe = h/mc and at the MIR λMIR=2πRMIR for characteristic energies of 1.1459x10-11 J* or 71.332 MeV and 1.1466x10-8 J* or 71.378 GeV* respectively.

    So we know that the Higgs-Mass-Induction occurs at those energy levels from the elementary template and as experimentally verified in terms of the neutrino masses by Super-Kamiokande in 1998.
    The LOR-energy of course indicates the Muon mass as a 'heavy electron' and the MIR-energy indicates the associated 'heavy quark' mass.

    This has been described before in the general mass induction scales for the diquarks as consequence from the bosonic bifurcation of string masses (XL-Boson string splits into quark- and lepton fermions as fundamental supersymmetry and the magnification of the Planck-scale).
    We also know, that the elementary proto-nucleon seed mc has grown in a factor of Yn~(1.618034)n~1.725 for a present np=1.1321711..to create the present nucleonmasses in a perturbation of its finestructure.

    Subsequently, the MIR-energy of 71.38 GeV represents a Zo-Boson seed, which has similarly increased between a factor of √(Ynp)~1.313292... and Ynp~1.72473589....

    These values so give present boundary conditions for the Higgs Boson in terms of its Zo coupling as the interval {93.74-123.09} GeV* or {93.51-122.79} GeV. The latter interval reduces by 1.58% to {92.03-120.85} GeV, as we have used the 'effective electron mass' me, differing in that percentage from the bare electron's restmass in our calculations.
    The lower bounded HB so manifests in the form of the Zo and as the majorana Higgs-Induction and coupled to the Spin-Induction of the Scalar Higgs Antineutrino.
    As described previously; the Zo-Boson mass is the mean of the top-quark K-Mean as 91.39165 GeV* = 91.167 GeV and so relates the quark energy levels to the Higgs inductions for both spin and inertia. This occurs at the down-strange ds-diquark level of the cosmogenesis.

    The W-Boson masses are the summation of the quark K-Means and represents the summation of all lower diquark energy levels from doubleup to doubledown.
    As the down-strange or MIR-LOR energy level is coupled as a Kernel-MIR level in the bottom-antibottom mesonic diquark system, the energy difference between the Zo- and the W-bosons should amount to that b-quark energy of about 10 GeV and which indeed is experimentally verified as such.
    Finally the doublestrange diquark level then becomes the well known Fermi-Energy of the Superquark K-Mean at 298.453 GeV*=297.717 GeV and which reduces to 293.013 GeV in the 1.58% in the SI mensuration system for an Fermi energy of 1.165x10-5 1/GeV2.

    Quantum Relativity then stipulates, that the Higgs-Mass-Induction energies will assume particular energy value related to the diquark mass induction table of the K-Means, coupled to the weakon masses as indicated.
    The overarching energy level is however that at 92 GeV as the lower bound and as represented in the definition of the Zo-Boson as a Majorana Spininduced scalar Higgs boson. The upper bound is the Fermi energy of the Super-Diquark as a doublestrange.
    This 92 GeV level represents a seedling energy of 71.38 GeV from the primordial universe and when the XL-Boson aka the heterotic string class HO(32) decayed into a fermionic quark-lepton bifurcation and which today is represented in the diquark eigenstates of the standard model in particle physics through its Unitary Symmetries.



    3.3 The Parametrisation of the Friedmann Equation

    It is well known, that the Radius of Curvature in the Field Equations of General Relativity relates to the Energy-Mass Tensor in the form of the critical density ρcritical = 3Ho2/8πG and the Hubble Constant Ho as the square of frequency or alternatively as the time differential of frequency df/dt as a cosmically applicable angular acceleration independent on the radial displacement.

    The scientific nomenclature (language) then describes this curved space in differential equations relating the positions of the 'points' in both space and time in a 4-dimensional description called Riemannian Tensor Space or similar.

    This then leads mathematically, to the formulation of General Relativity in Einstein's field Equations:

    einstein1-.37565.

    for the Einstein-Riemann tensor

    einstein2-.37566.

    and is built upon ten so-called nonlinear coupled hyperbolic-elliptic partial differential equations, which needless to say, are mathematically rather complex and often cannot be solved analytically without simplifying the geometries of the parametric constituents (say objects interacting in so called tensor-fields of stress-energy {Tμν} and curvatures in the Riemann-Einstein tensor {Gμν}, either changing the volume in reduction Ricci tensor {Rij} with scalar curvature R as {Rgμν} for the metric tensor {gμν} or keeping the volume of considered space invariant to volume change in a Tidal Weyl tensor {Rμν}).

    The Einstein-Riemann tensor then relates Curvature Radius R to the Energy-Mass tensor E=Mc2 via the critical density as 8πG/c4=3Ho2VcriticalMcriticalc2/Mcriticalc4 = 3Ho2Vcritical/c2 = 3Vcritical/R2 as Curvature Radius R by the Hubble Law applicable say to a nodal Hubble Constant Ho = c/RHubble.

    The cosmological field equations then can be expressed as the square of the nodal Hubble Constant and inclusive of a 'dark energy' terms often identified with the Cosmological Constant of Albert Einstein, here denoted LEinstein.
    Substituting the Einstein Lambda with the time differential for the square of nodal Hubble frequency as the angular acceleration acting on a quantized volume of space however; naturally and universally replaces the enigma of the 'dark energy' with a space inherent angular acceleration component, which can be identified as the 'universal consciousness quantum' directly from the standard cosmology itself.

    The field equations so can be generalised in a parametrization of the Hubble Constant assuming a cyclic form, oscillating between a minimum and maximum value given by Ho=dn/dt for cycletime n=Hot and where then time t is the 4-vector timespace of Minkowski lightpath x=ct.

    The Einstein Lambda then becomes then the energy-acceleration difference between the baryonic mass content of the universe and an inherent mass energy related to the initial condition of the oscillation parameters for the nodal Hubble Constant.

    ΛEinstein = GoMo/R(n)2 - 2cHo/(n+1)3 = Cosmological Acceleration - Intrinsic Universal Milgröm Deceleration as: gμνΛ = 8πG/c4 Tμν - Gμν

    then becomes Gμν + gμνL = 8πG/c4 Tμν and restated in a mass independent form for an encompassment of the curvature finestructures.


    Energy Conservation and Continuity:

    dE + PdV = TdS =0 (First Law of Thermodynamics) for a cosmic fluid and scaled Radius R=a.Ro; dR/dt = da/dt.Ro and d2R/dt2 = d2a/dt2.Ro

    dV/dt = {dV/dR}.{dR/dt} = 4πa2Ro3.{da/dt}

    dE/dt = d(mc2)/dt = c2.d{ρV}/dt = (4πRo3.c2/3){a3.dρ/dt + 3a2ρ.da/dt}

    dE + PdV = (4πRo3.a2){ρc2.da/dt + [ac2/3].dρ/dt + P.da/dt} = 0 for the cosmic fluid energy-pressure continuity equation:

    dρ/dt = -3{(da/dt)/a.{ρ + P/c2}} .........................................................................................(1)


    The independent Einstein Field Equations of the Robertson-Walker metric reduce to the Friedmann equations:

    H2 = {(da/dt)/a}2 = 8πGρ/3 - kc2/a2 + Λ/3 ...................................................................................(2)

    {(d2a/dt2)/a} = -4πG/3{ρ+ 3P/c2} + Λ/3 ..................................................................................(3)

    for scale radius a=R/Ro; Hubble parameter H = {da/dt)/a}; Gravitational Constant G; Density ρ; Curvature k ; light speed c and Cosmological Constant Λ.

    Differentiating (2) and substituting (1) with (2) gives (3):

    {2(da/dt).(d2a/dt2).a2 - 2a.(da/dt).(da/dt)2}/a4 = 8πG.(dρ/dt)/3 + 2kc2.(da/dt)/a3 + 0 = (8πG/3)(-3{(da/dt)/a.{ρ + P/c2}} + 2kc2.(da/dt)/a3 + 0

    (2(da/dt)/a).{(d2a/dt2).a - (da/dt)2}/a2 = (8πG/3){-3(da/dt)/a}.{ρ + P/c2} + 2{(da/dt)/a}.(kc2/a2) +0
    2{(da/dt)/a}.{(d2a/dt2).a - (da/dt)2}/a2 = 2{(da/dt)/a}{-4πG.{ρ + P/c2} + (kc2/a2)} +0 with kc2/a2= 8πGρ/3 + Λ/3 - {(da/dt)/a}2

    d{H2}/dt = 2H.dH/dt = 2{(da/dt)/a}.dH/dt
    dH/dt = {[d2a/dt2]/a - H2} = {-4πG.(ρ+ P/c2) + 8πGρ/3 + Λ/3 -H2} = -4πG/3(ρ + 3P/c2) + Λ/3 - H2} = -4πG/3(ρ + 3P/c2) + Λ/3 - 8πGρ/3 + kc2/a2 - Λ/3} = -4πG.(ρ + P/c2) + kc2/a2

    dH/dt = -4πG{ρ+P/c2} as the Time derivative for the Hubble parameter H for flat Minkowski spacetime with curvature k=0

    {(d2a/dt2).a - (da/dt)2}/a2 = -4πG{ρ+ P/c2} + (kc2/a2) + 0 = -4πG{ρ + P/c2} + 8πGρ/3 - {(da/dt)/a}2 + Λ/3

    {(d2a/dt2)/a} = (-4πG/3){3ρ + 3P/c2- 2ρ} = (-4πG/3){ρ + 3P/c2} + Λ/3 = dH/dt + H2

    For a scalefactor a=n/[n+1] = {1-1/[n+1]} = 1/{1+1/n}​

    dH/dt + 4πGρ = - 4πGP/c2 .... (for V4/10D=[4π/3]RH3 and V5/11D=2π2RH3 in factor 3π/2)

    areset = Rk(n)AdS/Rk(n)dS + ½ = n-∑∏nk-1+∏nk
    Scalefactor modulation at Nk={[n-∑∏nk-1]/Πnk } = ½ reset coordinate

    {dH/dt} = a