Blue Flower

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
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

2. The Inflaton
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)
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 Present Epoch in the initial Hubble Cycle
4.3 The Dark Matter - Baryon Matter Intersection
4.4 The Multiversal Hubble Cycles
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=1.13242 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 = 19.11 - 16.88 = 2.23 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.

Yn = RHubble/rWeyl = 2pRHubble/lWeyl = wWeyl/Ho = 2pnWeyl = nps/2p = 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 P nk = c/Ho P nk .....
nk = ln{wWeylRHubble(k)/c}/lnY = ln{wWeyl/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 scalefactored curvature radius R(n):

Lk (n) = GoMo/Rk(n)2 - 2cHo(Pnk)2/{n-SPnk-1+Pnk)3}

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

Lo = GoMo(n+1)2/RH2(n)2 - 2cHo/(n+1)3 L1 = GoMo(n-1+n1)2/n12RH2(n-1)2 - 2cHon12/(n-1+n1)3 L2 = GoMo(n-1-n1+n1n2)2/n12n22RH2(n-1-n1)2 - 2cHon12n22/(n-1-n1+n1n2)3 .....

and where

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

Lo/adeBroglie = GoMo/Rk(n)2/PnkRHfps2 = {GoMo(n-SPnk-1+Pnk)2/{[Pnk]2.RH2(n-SPnk-1)2(PnkRHfps2)} = (PnkWo

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

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

with nps = 2pPnk-1.Xnk = lps/RH = Hotps = Ho/fps = ctps/RHand 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/Pnk=(n-SPnk-1)/Pnk tk = t - (1/Ho)SPnk-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) = PnkRH(n-SPnk-1)/{n-SPnk-1+Pnk}

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

Vk(n) = dRk(n)/dt = c{Pnk}2/{n-SPnk-1+Pnk}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(Pnk)2/(n-SPnk-1+Pnk)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

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 L(n) for Lps=LQBB=GoMo/lps2 and where the wavelength of the de Broglie matter wave of the inflaton lps 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 + 4pGr = - 4pGP/c2

... (for V4/10D=[4p/3]RH3 and V5/11D=2p2RH3 in factor 3p/2)
For Hypersphere Volumar of 3-sphere: d2{V4}/dR2 = d2p2R4}/dR2 = d{2p2R3}/dR = 6p2R2 Surface Area of Horn Torus (2pR)(2pR)= 4p2R2

Linearisation of lps = 2prps = npsRH = c/fps = HoRH/fps
4pMo/R3 = Mo/{2p2(lps/2p)3} = Mo/{4p2{lps/2p}3 for Eps ZPE/VPE density 4pEps/rps3
{4pMo/R3}.{3p/2} = 3Mo/{4p(lps/2p)3} = 6p2Mo/lps3 = 4p.{3p/2}Mo/lps3 = 4p.dFeigenbaum chaos limit {Mo/lps3}

areset = Rk(n)AdS/Rk(n)dS + ½ = n-SPnk-1+Pnk +½ Scalefactor modulation at Nk = {[n-SPnk-1]/Pnk } = 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 + 4pGr = - 4pGP/c2

-Ho2(2n+1)(n+3/2)/T(n)2 + GoMo/{RH3(n/[n+1])3}{4p} = L(n)/{RH(n/[n+1])} + L/3 -2Ho2{[n+1]2-¼}/T[n]2 + GoMo/RH3(n/[n+1])3{4p} = L(n)/RH(n/[n+1]) + L/3 -2Ho2{[n+1]2-¼}/T(n)2 + 4p.GoMo/RH3(n/[n+1])3 = L(n)/RH(n/[n+1]) + L/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=1.13242:............ - (+6.7003x10-11 J/m3)* = (2.12682x10-11 J/m3)* + (-8.82709x10-11 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=-0.5585, the DE Lambda calculates as -6.700x10-11 (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 = lps/2p, the critical modulated Schwarzschild radius rss = 2plss = 2px1022 m* for lps = 1/lss and for an applied scalefactor a = n/[n+1] = lss/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) = 6π2lps2.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/(2p2sRH2[550n3/[n+1]2]) for T(n)4 = {[n+1]2/n3}HoMoc2/(2p2sRH2[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. CurvatureAdS.

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/2MWBMps; 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 rP=lP3/mP=1.85x1096 and the 'critical closure' density rH=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).


Describing the Einstein Lambda in the form of a parametrized Curvature Radius L(n)/RHubble= L(n)Ho/c = L(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. Brane mirror duality unifies the electromagnetic and gravitational interactions via the coupling of their finestructures. 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) selfstates.
The 'vibratory' selfstate is denoted in: Eps=Eprimary sourcesink=hfps=mpsc2 and the 'winding' and coupled selfstate is denoted by: Ess=Eecondary 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 Supermembrane EpsEss then denotes the coupled superstrings in their 'vibratory' high energy and 'winded' low energy selfstates.
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 Finestructure: ae = 2pke2/hc = e2/2e0hc
Gravitational Finestructure (Electron): ag = 2pGome2/hc = {me/mPlanck}2
Gravitational Finestructure (Primordial Nucleon): an = 2pGomc2/hc
Gravitational Finestructure (Planck Boson): aPlanck = 2pGomPlanck2/hc

1/Eps=e*=2Rec2=√{4αhce2/2πGome2}=2e√α[mP/me=2e√{ae/ag} = {2e2/me}√(k/Go)=2e2/Gome = e2/2peome for Go = 1/k = 4peo for the cosmological unification of the finestructures.
Eps = 1/Ess = 1/e* = {ag/ae}/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=e2/4peomec2 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?"


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 {w=2pGomPlanck2/hc} via ke2 = e2/4peo = 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 = mo.eo = {120p/c}{1/120pc} and 'Free Space' Inflaton Impedance Zo= electric field strength E/magnetic field strength H = √(mo/eo) = cmo = 1/ceo = 120p}.

[Go]mod =[4peo]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 w=1 defines the Planck-Mass and setting a proto-nucleon seed mc=mPlanck.a9 allows the breaking of the inflaton supersymmetry in the superstring classes.
Replacing the protonucleon mass mc = √{hc/2pGo}.{60pe2/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.


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 = lmin.fmax = 2pRmin.fmax as lightspeed invariance for the vibratory string mode Rcurvature = Rmin = lmin /2p = Wormhole Perimeter/2p

1/c = 1/(lmin.fmax) = lmax.fmin = lmax/fmax = Rmax.fmin/2p as lightspeed invariance for the winding string mode Rcurvature = Rmax = 2p.lmax = 2p/Wormhole Perimeter

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

Planck Mass = mPlanck = √{hc/2pGo}
Planck Energy = EPlanck = mPlanck.c2 = √{hc5/2pGo} = hfPlanck = hc/lPlanck = kTPlanck
Planck Length = lPlanck = lPlanck/2p = √{hGo/2pc3}
Planck Temperature = TPlanck = EPlanck/k = √{hc5/2pk2Go}
Planck Density = ρPlanck= mPlanck/VPlanck = √{4p2c10/h2Go4}/2p2 = c5/phGo2= 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/2pGo)(2pc3/hGo)}(2pc3/hGo)(rwormhole3/mwormhole} = (c2/Go)(2pc3/hGo){rwormhole3/mwormhole}
= (2pc5/hGo2){rwormhole3/mwormhole} = {4p2k2/h2Go} (hc5/2pGok2){rwormhole3/mwormhole} = {kTPlanck}2(2prwormhole)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: ldeBroglie = 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: ldeBroglie = 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/ldeBroglie and for a relativistic de Broglie wavelength, 60% smaller, than for the nonrelativistic electron in ldeBroglie = h/1.333..moc < h/0.8moc = ldeBroglie (1.83x10-12 m relativistic and 3.05x10-12 m nonrelativistic 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/ldeBrogliec2 = h/ldeBrogliec = mdeBroglie = [Action as Charge2]mod/c(Planck-Length Oscillation)
= [2pe2]mod/cldPlanck√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 rps=lps/2p = Gomps/c2

The factor 2Go/c2 multiplied by the factor 4p becomes Einstein's Constant k = 8pGo/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]modk for a proportionality constant
{k*}=2Re/30k[ec]mod = 2Re.c2/8pe = e*/8pe =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 = Smss = n.{h/2prdeBrogliec} .[Ess.e*]mod = n.mps.[Ess.{9x1060}.2p2Rrmp3]mod = n.mps.[Ess.{2Re.c2}]mod = n.[Eps.Ess]mod.[2Re]mod
for ldeBroglie=lps=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=1/4peo = 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 1.44133588x10-34rps 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 = Smss = n.{mps} .[Ess.e*]mod = n.{mps}[{hfss}{fps/fss}.2p2Rrmp3]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*/4pGo = 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 = 10-22/2p 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*/4pGo.mps = NAvagadro-Instanton = rps/Rps
NAvagadro-Instanton = 5.8012x1023
for hypermass
MHyper = hc3.e*/4pGo = 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*/4pGo}/mmin = {n.rminc2/2Go}/mmin = {hc3.c2/4pGoEmin}{ne*} = {hc3.c2/4pGohfmin}{ne*} = {2prmin.hc3.c2/4pGohc}{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.lmin.

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

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 m = 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 = 1.711512476..x10-27 kg 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/2pGo}{½mPlanck.c2/k} = hc3/4pGok = {MSmin.TSmax} = {mps.Tps.½NAvagadro-Instanton} = [c2/4p2]mod.{MMaxHawking .TSmin }
= 9.131793821x1023 kgK with (mpsTps = Eps2/kc2 = 1.002117..p)

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*/4pGo = ½NAvagadro-Instanton.mwormhole = 6445.775 kg at the Instanton boundary n=nps so increases to MHyper(npresent)Ynpresent =hc3.e*/4pGoXnpresent ~ 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=1.1324.. for a decreased perturbed G(npresent) = 6.443x10-11 G-string units for the Standard Gravitational Parameter G(n)miYk(n).mjYn-k = Gomc2 = constant for G(n)=GoXn.[/b]

For a present measured neutron mass of 1.674927x10-27 kg = 939.5656 MeV in the [SI} system of measurement, the string values are (1.674927x10-27)(1.003753127) = 1.681212..x10-27 kg* or (939.5656)(1.005102826){e-/e-*} = (939.5656)(1.005102764)/(1.002671189) = 941.844 MeV*

Using the λminλmax=1 wavelength modulation in the T/Mirror 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 ~ 0.9989...
(More details are described in 7. Newton's Gravitational Constant Measurements following. this excerpt.)

"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.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=Gom c²/mnmax.mnmin=Gomc²/({mcYn}{mnmin}) and where we have mnmin=mcYk} for the unknown value of k.

So Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking.mav}} and where now {mnmin}={mcYk}={8π.M.MHawking.mav/Mo2}=1.0011..mav.
mav={Mo²/8π.M.MHawking}{mnmin}={Mo²/8π.M.MHawking}{mcYk}=0.9989..{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}{mcY2n/mN2} and where {Mo2/8π.M.MHawking = 0.9989..}

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.

For a Neutron Restmass of: mn=1.680717x10-27 kg* (941.6036 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)=6.678764x10-11 (m3/kgs2) and a perturbation corrected mn=1.681100563x10-27 kg* (941.818626 MeV*) gives: mneutron = 1.67481477x10-27 kg

G(np) = Go{mc/mN}2.(0.9989..) = 6.67093x10-11 (m3/kgs2)* or 6.675547x10-11 (m³/kgs²).

The perturbation upper limit is given in the mn=1.681335x10-27 kg* (941.9506 MeV*) and gives:
G(np) = Go{mc/mN}2.(0.9989..) = 6.6690685x10-11 (m3/kgs2)* or 6.673685x10-11 (m³/kgs²).

The average for the last two values then approximates as a 'best fit' for:
Gm(np) = ½{6.67093x10-11 + 6.6690685x10-11} (m3/kgs2)* = 6.6699925x10-11 (m3/kgs2)*
or Gm(np) = ½{6.675547x10-11 + 6.673685x10-11} (m3/kgs2) = 6.674816x10-11 (m3/kgs2)

This is a best-fit approximation, considering the uncharged nature of the testmasses.
This then gives the value of k from Gm(n)=Go.Xn+k as k=ln(GmYn/Go)/lnX and which calculates as k= -0.073387.."