A Revision of the Friedmann Cosmology

A Revision of the Friedmann Cosmology

1. 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 ρ_critical = 3H_o²/8πG and the Hubble Constant H_o 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 Riemann Tensor Space or similar.

This then leads mathematically, to the formulation of General Relativity in Einstein's field Equations:

for the Einstein-Riemann tensor


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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 {T_μν} and curvatures in the Riemann-Einstein tensor {G_μν}, either changing the volume in reduction of the Ricci tensor {R_ij} with scalar curvature R as {Rg_μν} for the metric tensor {g_μν} or keeping the volume of considered space invariant to volume change in a Tidal Weyl tensor {R_μν}).

The Einstein-Riemann tensor then relates Curvature Radius R to the Energy-Mass tensor E=Mc² via the critical density as 8πG/c⁴=3H_o²V_critical.M_critical.c²/M_critical.c⁴ = 3H_o²V_critical/c² = 3V_critical/R² as Curvature Radius R by the Hubble Law applicable say to a nodal Hubble Constant H_o = c/R_Hubble.

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 Λ_Einstein.
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 H_o=dn/dt for cycle time n=H_ot and where then time t is the 4-vector time-space of Minkowski light-path 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.

Λ_Einstein = G_oM_o/R(n)² - 2cH_o/(n+1)³ = Cosmological Acceleration - Intrinsic Universal Milgröm Deceleration as: g_μνΛ = 8πG/c⁴ T_μν - G_μν

then becomes G_μν + g_μνΛ = 8πG/c⁴ T_μν and restated in a mass independent form for an encompassment of the curvature fine structures.


Energy Conservation and Continuity:

dE + PdV = TdS =0 (First Law of Thermodynamics) for a cosmic fluid and scaled Radius R=a.R_o; dR/dt = da/dt.R_o and d²R/dt² = d²a/dt².R_o

dV/dt = {dV/dR}.{dR/dt} = 4πa²R_o³.{da/dt}

dE/dt = d(mc²)/dt = c².d{ρV}/dt = (4πR_o³.c²/3){a³.dρ/dt + 3a²ρ.da/dt}

dE + PdV = (4πR_o³.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/R_o; 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 space-time 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 scale factor a=n/[n+1] = {1-1/[n+1]} = 1/{1+1/n}​

dH/dt + 4πGρ = - 4πGP/c² .... (for V_4/10D=[4π/3]R_H³ and V_5/11D=2π²R_H³ in factor 3π/2)

a_reset = R_k(n)_AdS/R_k(n)_dS + ½ = n-∑∏n_k-1+∏n_k +½

Scale factor modulation at N_k={[n-∑∏n_k-1]/Πn_k } = ½ reset coordinate

{dH/dt} = a_reset .d{H_o/T(n)}/dt = - H_o²(2n+1)(n+3/2)/T(n)² for k=0

dH/dt + 4πGρ = - 4πGP/c²

-H_o²(2n+1)(n+3/2)/T(n)² + G_oM_o/{R_H³(n/[n+1])³}{4π} = Λ(n)/{R_H(n/[n+1])} + Λ/3
-2H_o²{[n+1]²-¼}/T[n]² + G_oM_o/R_H³(n/[n+1])³{4π} = Λ(n)/R_H(n/[n+1]) + Λ/3
-2H_o²{[n+1]²-¼}/T(n)² + 4π.G_oM_o/R_H³(n/[n+1])³ = Λ(n)/R_H(n/[n+1]) + Λ/3

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

Λ(n)/R_H(n/[n+1]) = - 4πGP/c² = G_oM_o/R_H³(n/[n+1])³ -2H_o²/(n[n+1]²)

and Λ = 0
for -P(n) = Λ(n)c²[n+1]/4πG_onR_H = Λ(n)H_oc[n+1]/4πG_on = M_oc²[n+1]³/4πn³R_H³ - H_o²c²/2πG_on[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 (cH_o/G_o)​

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 q_dS=-0.5586, the DE Lambda calculates as -6.696x10^-11 (N/m²=J/m³)*, albeit as a positive pressure within the negative quintessence.


2. An expanding multi-dimensional super-membraned open and closed Universe


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 space time in a multi timed connector dimension.
The resulting multiverse or brane world 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 time space but co-local in its lower dimensional Minkowski space-time.

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 space-time in 12-dimensional brane space (F-Vafa 'bulk' Omnispace) with positive spheroidal curvature k=+1 and cancels with its inner boundary as a negatively curved k=-1 hyperbolic AdS space-time in 11 dimensions to form the observed 4D/10-dimensional zero curvature dS space-time, encompassed by the first Calabi Yau manifold.

A bounded (sub) 4D/10D dS space-time then is embedded in a Anti de Sitter (AdS) 11D-space-time of curvature k=-1 and where 4D dS space-time 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 and images the positive curvature in 12D-F-Vafa space in a 'convex lense' effect of 11-dimensional M-Witten spacetime.

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Rps = λps/2π as the wormhole radius of the Instanton as a conformally transformed Planck-Length L_p = √{G_oh/2πc³} from the Inflaton.
The Schwarzschild metric for 2L_p = 2G_oM_p/c² transforms a 3D Planck-length in the Planck-mass M_p = √{hc/2πG_o} from the Planck-boson gravitational fine structure constant 1 = 2πG_oM_p²/hc.

The Schwarzschild metric for the Weyl-wormhole radius R_ps then defines a hypermass M_hyper as the conformal mapping of the Planck-mass M_p as M_hyper = ½{R_ps/L_p}M_p = ½{R_ps/L_p}².M_ps and where M_ps = E_ps/c² = hf_ps/c² = kT_ps/c² in fundamental expressions for the energy of Abba-E_ps as one part of the super membrane E_ps.E_ss in physical quantities of mass m, frequency f and temperature T.

c² and h and k are fundamental constants of nature obtained from the initializing algorithm of the Mathimatia and are labeled as the 'square of lightspeed c' and 'Planck's constant h' and 'Stefan-Boltzmann's constant k' respectively. The complementary part of super membrane E_psE_ss is EssBaab. Eps-Abba is renamed as 'Energy of the Primary Source-Sink' and Ess-Baab is renamed as 'Energy of the Secondary Sink-Source'. The primary source-sink and the primary sink-source are coupled under a mode of mirror-inversion duality with Eps describing a vibratory and high energy micro-quantum quantum entanglement with Ess as a winding and low energy macro quantum energy. It is this quantum entanglement, which allows Abba to become part of Universe in the encompassing energy quantum of physicalized consciousness, defined in the magnetopolar charge.

The combined effect of the applied Schwarzschild metric then defines a Compton Constant to characterize the conformal transformation as: Compton Constant h/2πc = MpLp = MpsRps. Quantum gravitation now manifests the mass differences between Planck-mass M_p and Weyl mass M_ps. The Black Hole physics had transformed M_p from the definition of L_p; but this transformation did not generate M_ps from R_ps, but rather hypermass M_hyper, differing from M_ps by a factor of ½{R_ps/L_p}².

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 space-time and the third the dynamic lightpath bound for the Hubble Event horizon in 5D/11D AdS time-space.
The completion of a 'de Broglie wave matter' evolution cycle triggers the Hubble Event Horizon as the inner boundary of the time-space mirrored Calabi Yau manifold to quantum tunnel onto the outer boundary of the space-time mirrored Calabi Yau manifold in a second universe; whose inflaton was initiated when the light-path in the first universe reached its second Hubble node.

For the first universe, the three nodes are set in time-space as {3.3x10^-31 s; 16.88 Gy; 3.96 Ty} and the second universe, time shifted in t₁=t_o+t with t_o=1/H_o has a nodal configuration {t_o+1.4x10^-33; t_o+3,957 Gy; t_o+972.7 Ty}; the latter emerging from the time-space as the instanton at time marker t_o.
A third universe would initiate at a time coordinate t₂=t_o+t₁+t as {1/H_o+234.472/H_o +5.8x10^-36 s; t_o+t₁+972.7 Ty; t_o+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 time-space coordinate at 3,974.8 billion years from the time instanton aka the Quantum Big Bang.

For a present time-space coordinate of n_present=1.13271 however; all information in the first universe is being mirrored by the time-space of the AdS space-time into the dS space-time of the second universe at a time frame of t = t₁-t_o = 19.12 - 16.88 = 2.24 billion years and a multi-dimensional 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.

View: https://youtu.be/RF7dDt3tVmI
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Yⁿ = R_Hubble/r_Weyl = 2πR_Hubble/λ_Weyl = ω_Weyl/H_o = 2πn_Weyl = n_ps/2π = 1.003849x10⁴⁹

2nd Inflaton/Quantum Big Bang redefines for k=1: R_Hubble(1) = n₁R_Hubble = c/H_o(1) = (234.472)R_Hubble = 3.746x10²⁸ m* in 3.957 Trillion Years for critical n_k
3rd Inflaton/Quantum Big Bang redefines for k=2: R_Hubble(2) = n₁n₂R_Hubble = c/H_o(2) = (234.472)(245.813)R_Hubble = 9.208x10³⁰ m* in 972.63 Trillion Years for critical n_k
4th Inflaton/Quantum Big Bang redefines for k=3: R_Hubble(3) = n₁n₂n₃R_Hubble = c/H_o(3) = (57,636.27)(257.252)R_Hubble = 2.369x10³³ m* in 250.24 Quadrillion Years for critical n_k
5th Inflaton/Quantum Big Bang redefines for k=4: R_Hubble(4) = n₁n₂n₃n₄R_Hubble = c/H_o(4) = (14,827,044.63)(268.785)R_Hubble = 6.367x10³⁵ m* in 67.26 Quintillion Years for critical n_k
...
(k+1)th Inflaton/Quantum Big Bang redefines for k=k: R_Hubble(k) = R_Hubble Π n_k = c/H_o Π n_k
.....

n_k = ln{ω_WeylR_Hubble(k)/c}/lnY = ln{ω_Weyl/H_o(k)}/lnY

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


Dark Energy DE-Quintessence Λ_k 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):


Λ_k (n) = G_oM_o/R_k(n)² - 2cH_o(Πn_k)²/{n-ΣΠn_k-1+Πn_k)³} for negative Pressure P_k = -Λ_k(n)c²/4πG_oR_k

= {G_oM_o(n-ΣΠn_k-1+Πn_k)²/{(Πn_k)².R_H²(n-ΣΠn_k-1)²} - 2cH_o(Πn_k)²/{n-ΣΠn_k-1+Πn_k)³}

Λ_o = G_oM_o(n+1)²/R_H²(n)² - 2cH_o/(n+1)³
Λ₁ = G_oM_o(n-1+n₁)²/n₁²R_H²(n-1)² - 2cH_on₁²/(n-1+n₁)³
Λ₂ = G_oM_o(n-1-n₁+n₁n₂)²/n₁²n₂²R_H²(n-1-n₁)² - 2cH_on₁²n₂²/(n-1-n₁+n₁n₂)³
.....

Lambda-DE-Quintessence Derivatives:

Λ_k'(n) = d{Λ_k}/dn =
{G_oM_o/Πn_k²R_H²}{2(n-ΣΠn_k-1+Πn_k).(n-ΣΠn_k-1)² - 2(n-ΣΠn_k-1).(n-ΣΠn_k-1+Πn_k)²}/{(n-ΣΠn_k-1)⁴} - {-6cH_o(Πn_k)²}/(n-ΣΠn_k-1+Πn_k)⁴

= {-2G_oM_o/Πn_kR_H²}(n-ΣΠn_k-1+Πn_k)/(n-ΣΠn_k-1)³ + {6cH_o(Πn_k)²}/(n-ΣΠn_k-1+Πn_k)⁴

= {6cH_o(1)²}/{(n-0+1)⁴} - {2G_oM_o/1.R_H²}{(n-0+1)/(n-0)³}........................................ for k=0
= {6cH_o(1.n₁)²}/{(n-1+n₁)⁴} - {2G_oM_o/n₁.R_H²}{(n-1+n₁)/(n-1)³}................................ for k=1
= {6cH_o(1.n₁.n₂)²}/{(n-1-n₁+n₁.n₂)⁴} - {2G_oM_o/n₁n₂.R_H²}{(n-1-n₁+n₁n₂)/(n-1-n₁)³}...... for k=2
.......

For k=0; {G_oM_o/3c²R_H} = constant = n³/[n+1]⁵
for roots n_Λmin = 0.23890175.. and n_Λmax = 11.97186...
{G_oM_o/2c²R_H} = constant = [n]²/[n+1]⁵

for Λ_o-DE roots: n_+/- = 0.1082331... and n_-/+ = 3.40055... for asymptote Λ_0∞ = G_oM_o/R_H² = 7.894940128...x10^-12 (m/s²)*

For k=1; {G_oM_o/3n₁³c²R_H} = constant = [n-1]³/[n-1+n₁]⁵ = [n-1]³/[n+233.472]⁵
for roots n_Λmin = 7.66028... and n_Λmax = 51,941.9..
{G_oM_o/2n₁⁴c²R_H} = 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 Λ_1∞ = G_oM_o/n₁²R_H² = 1.43604108...x10^-16 (m/s²)*


For k=2; {G_oM_o/3n₁³n₂³c²R_H} = constant = [n-1-n₁]³/[n-1-n₁+n₁n₂]⁵ = [n-235.472]³/[n+57,400.794]⁵
for roots n_Λmin = 486.7205 and n_Λmax = 2.0230105x10⁸
{G_oM_o/2n₁⁴n₂⁴c²R_H} = 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 Λ_2∞ = G_oM_o/n₁²n₂²R_H² = 2.37660590...x10^-21 (m/s²)*

For k=3; {G_oM_o/3n₁³n₂³n₃³c²R_H} = constant = [n-1-n₁-n₁n₂]³/[n-1-n₁-n₁n₂+n₁n₂n₃]⁵ = [n-57,871.74]³/[n+1.47691729x10⁷]⁵
for roots n_Λmin = 67,972.496 and n_Λmax = 8.3526797...x10¹¹
{G_oM_o/2n₁⁴n₂⁴n₃⁴c²R_H} = 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 Λ_3∞ = G_oM_o/n₁²n₂²n₃²R_H² = 3.59120049...x10^-26 (m/s²)*



and where

Πn_k=1=n_o and Πn_k-1=0 for k=0
with Instanton/Inflaton resetting for initial boundary parameters

Λ_o/a_deBroglie = {G_oM_o/R_k(n)²}/Πn_kR_Hf_ps²
= {G_oM_o(n-ΣΠn_k-1+Πn_k)²}/{[Πn_k]².R_H²(n-ΣΠn_k-1)²(Πn_kR_Hf_ps²)} = (Πn_k)½Ω_o

for Instanton-Inflaton Baryon Seed Constant Ω_o = M_o*/M_H* = 0.02803 for the kth universal matter evolution

k=0 for Reset n=n_ps=H_ot and Λ_o/a_deBroglie = G_oM_o(n_ps+1)²/{R_H³n_ps²(f_ps²)} = G_oM_o/R_Hc² = M_o/2M_H = ½Ω_o
k=1 for Reset n=1+n_ps and Λ_o/a_deBroglie = G_oM_o(1+n_ps-1+n₁)²/{[n₁]².R_H³(1+n_ps-1)²(n₁f_ps²)} = M_o/2n₁M_H = M_o/2M_H* = ½Ω_o*
k=2 for Reset n=n₁+1+n_ps and Λ_o/a_deBroglie = G_oM_o(n₁+1+n_ps-1-n₁+n₁n₂)²/{[n₁n₂]².R_H³(n₁+1+n_ps-1-n₁)²(n₁n₂f_ps²)} = ½Ω_o**
k=3 for Reset n=n₁n₂+n₁+1+n_ps and Λ_o/a_deBroglie = G_oM_o(n₁n₂+n₁+1+n_ps-1-n₁-n₁n₂+n₁n₂n₃)²/{[n₁n₂n₃]².R_H³(n₁n₂+n₁+1+n_ps-1-n₁-n₁n₂)²(n₁n₂n₃f_ps²)} = ½Ω_o***
......

with n_ps = 2πΠ_nk-1.X^n_k =λ_ps/R_H = H_ot_ps = H_o/f_ps = ct_ps/R_H and R_H=2G_oM_H/c²

N_o=H_ot_o/n_o=H_ot=n
N₁=H_ot₁/n₁=(n-1)/n₁
N₂=H_ot₂/n₁n₂=(n-1-n₁)/n₁n₂
N₃=H_ot₃/n₁n₂n₃=(n-1-n₁-n₁n₂)/n₁n₂n₃
....
dn/dt=H_o
.....

N_k=H_ot_k/Πn_k=(n-ΣΠn_k-1)/Πn_k
t_k = t - (1/H_o)ΣΠn_k-1 for n_o=1 and N_o=n

t_o=t=n/H_o=N_o/H_o=nR_H/c
t₁=t-1/H_o=(n-1)/H_o=[n₁N₁]/H_o
t₂=t-(1+n₁)/H_o=(n-1-n₁)/H_o=(n₁n₂N₂)/H_o
t₃=t-(1+n₁+n₁n₂)/H_o=(n-1-n₁-n₁n₂)/H_o=(n₁n₂n₃N₃)/H_o
.......

R(n)=R(N_o)=n_oR_H{n/[n+1]}=R_H{n/[n+1]}
R₁(N₁)=n₁R_H{N₁/[N₁+1]}=n₁R_H{[n-1]/[n-1+n₁]}
R₂(N₂)=n₁n₂R_H{N₂/[N₂+1]}=n₁n₂R_H{[n-1-n₁]/[n-1-n₁+n₁n₂]}
R₃(N₃)=n₁n₂n₃R_H{N₃/[N₃+1]}=n₁n₂n₃R_H{[n-1-n₁-n₁n₂]/[n-1-n₁-n₁n₂+n₁n₂n₃}
.......


R_k(n) = Πn_kR_H(n-ΣΠn_k-1)/{n-ΣΠn_k-1+Πn_k}

.....= R_H(n/[n+1]) = n₁R_H(N₁/[N₁+1]) = n₁n₂R_H(N₂/[N₂+1]) =.....



V_k(n) = dR_k(n)/dt = c{Πn_k}²/{n-ΣΠn_k-1+Πn_k}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 =.....



A_k(n) = d²R_k(n)/dt² = -2cH_o(Πn_k)²/(n-ΣΠn_k-1+Πn_k)³

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

G_oM_o is the Gravitational Parameter for the Baryon mass seed; Curvature Radius R_H = c/H_o in the nodal Hubble parameter H_o and c is the speed of light


Hubble Parameters:

H(n)|_dS = {V_k(n)}/{R_k(n)} = {c[Πn_k]²/[n-ΣΠn_k-1+Πn_k]²}/{Πn_k.R_H[n-ΣΠn_k-1]/(n-ΣPn_k-1+Πn_k)} = Πn_kH_o/{[n-ΣΠn_k-1][n-ΣΠn_k-1+Πn_k]}


H(n)|_dS = Πn_kH_o/{[n-ΣΠn_k-1][n-ΣΠn_k-1+Πn_k]}

.....= H_o/{[n][n+1]}=H_o/T(n) = n₁H_o/{[n-1][n-1+n₁]} = n₁n₂H_o/{[n-1-n₁][n-1-n₁+n₁n₂]} =..... for dS

H(n)'|_dS = H_o/[n-ΣΠn_k-1] for oscillating H'(n) parameter between nodes k and k+1 ||n_ps+ΣΠn_k-1 - ΣΠn_k||

H(n)|_AdS = H(n)'|_AdS = {V_k(n)}/{R_k(n)} = c/{R_H(n-ΣΠn_k-1)}

H(n)|_AdS = H(n)' = H_o/(n-ΣΠn_k-1)

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


For initializing scale modulation R_k(n)_Ads/R_k(n)_dS + ½ = Πn_kR_H(n-ΣΠn_k-1)/{Πn_kR_H(n-ΣΠn_k-1)/(n-ΣΠn_k-1+Πn_k)} + ½Πn_k = {n - ΣΠn_k-1 + Πn_k + ½} reset coordinate

dH/dt = (dH/dn)(dn/dt) = -Πn_k.H_o²{(2n-2ΣΠn_k-1+Πn_k)(n-ΣΠn_k-1+Πn_k+½Πn_k)}/{n²-2nΣΠn_k-1+(ΣΠn_k-1)²+Πn_k[n-ΣΠn_k]}²
= -2Πn_kH_o²{[n - ΣΠn_k-1 + Πn_k]² - ¼ΣΠn_k²}/{(n-ΣΠn_k-1)(n-ΣΠn_k-1+Πn_k)}²

dH/dt|_dS = -2Πn_kH_o²{[n - ΣΠn_k-1 + Πn_k]² - ¼(ΣΠn_k)²}/{(n-ΣΠn_k-1)(n-ΣΠn_k-1+Πn_k)}²


.....= -2H_o²([n+1]²-¼)/{n[n+1]}² = -2n₁H_o²{[n-1+n₁]²-¼n₁²}/{[n-1][n-1+n₁]}² = -2n₁n₂H_o²{[n-1-n₁+n₁n₂]²-¼n₁²n₂²}/{[n-1-n₁][n-1-n₁+n₁n₂]}² =.....



dH/dt = (dH/dn)(dn/dt) = -H_oc/{(R_H(n-ΣΠn_k-1)²} = -H_o²/{n-ΣΠn_k-1}² for AdS

dH/dt|_AdS = -H_o²/{n-ΣΠn_k-1}²

.....= -H_o²/n² = H_o²/(n-1)² = -H_o²/(n-1-n₁)² = .....



dH/dt + 4πG_oρ = - 4πG_oP/c²

dH/dt + 4πG_oM_o/R_k(n)³ = Λ_k(n)/R_k(n) = - 4πG_oP/c² = G_oM_o/R_k(n)³ - 2(Πn_k)H_o²/{(n-ΣΠn_k-1)(n-ΣΠn_k-1+Πn_k)²} for dS with

{-4π}P(n)|_dS = M_oc²/R_k(n)³ - 2Πn_k(H_oc)²/{G_o(n-ΣΠn_k-1)(n-ΣΠn_k-1+Πn_k)²} = M_oc²(n-ΣΠn_k-1+Πn_k)³/{Πn_k.R_H(n-ΣΠn_k-1)}³ - 2Πn_kH_o²c²/{G_o(n-ΣΠn_k-1)(n-ΣΠn_k-1+Πn_k)²}



Λ_k(n)/R_k(n) = -4πG_oP/c² = G_oM_o/R_k(n)³ - dH/dt = G_oM_o/{R_H(n-ΣΠn_k-1)}³ - H_o²/{n-ΣΠn_k-1}² for AdS with

{-4π}P(n)|_AdS = M_oc²/R_k(n)³ - (H_oc)²/{G_o(n-ΣΠn_k-1)²} = M_oc²/{R_H(n-ΣΠn_k-1)}³ - H_o²c²/{G_o(n-ΣΠn_k-1)²}




Deceleration Parameters:

q_AdS(n) = -A_k(n)R_k(n)/V_k(n)² = -{(-2cH_o[Πn_k]²)/(n-ΣΠn_k-1+Πn_k)³}{Πn_kR_H(n-ΣΠn_k-1)/(n-ΣΠn_k-1+Πn_k)}/{[Πn_k]²c/(n-ΣΠn_k-1+Πn_k)}² = 2(n-ΣΠn_k-1)/Πn_k

q_AdS+dS(n) = 2(n-ΣΠn_k-1)/Πn_k

q_dS(n) = 1/q_AdS+dS(n) - 1 = Πn_k/{2[n-ΣΠn_k-1} - 1

with A_k(n)=0 for AdS in a_reset = R_k(n)_AdS/R_k(n)_dS + ½ = {R_H(n-ΣΠn_k-1)}/{R_H(n-ΣΠn_k-1)/(n-ΣΠn_k-1+1)} + ½ = n-ΣΠn_k-1+1+½


Scalefactor modulation at N_k = {n-ΣΠn_k-1}/Πn_k = 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 q_dS=1 with q_AdS=1

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




Temperature:

T(n) =∜{M_oc²/(1100σπ².R_k(n)².t_k)} and for t_k = (n-ΣΠn_k-1)/H_o

T_k(n) = ∜{H_oM_oc²(n-ΣΠn_k-1+Πn_k)²/[1100σπ².R_H².(n-ΣΠn_k-1)³]}
=∜{(H_o³M_o(n-ΣΠn_k-1+Πn_k)²)/[1100σπ²(n-ΣΠn_k-1)³]} = ∜{18.199(n-ΣΠn_k-1+Πn_k)²/(n-ΣΠn_k-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-ΣΠn_k-1+Πn_k]²+[Πn_k]²)/([n-ΣΠn_k-1+Πn_k]²-[Πn_k]²)} =
√{([n-ΣΠn_k-1]²+2Πn_k(n-ΣΠn_k-1)+2(Πn_k)²)/([n-ΣΠn_k-1]²+2Πn_k(n-ΣΠn_k-1)} = √{1 + 2(Πn_k)²/{(n-ΣΠn_k-1)(n-ΣΠn_k-1+2Πn_k)}

z+1 = √{ 1 + 2/{[n²-2nΣΠn_k-1 +(ΣΠn_k-1)²+2n-2ΣΠn_k-1} = √{1+2/{n(n+2-2ΣΠn_k-1) + ΣΠn_k-1(ΣΠn_k-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:

Ω_DM = 1-Ω_BM until Saturation for BM-DM and Dark Energy Separation

ρ_BM+DM/ρ_critical = Ω_oY^{{[n-ΣΠn_k-1]/Πn_k}}/{(n-ΣΠn_k-1)/(n-ΣΠn_k-1+Πn_k)}³ = M_oY^{{[n-ΣΠn_k-1]/Πn_k}}/{ρ_criticalR_k(n)³}

Baryon Matter Fraction Ω_BM = Ω_oY^{N_k} = Ω_o.Y^{{[n-ΣΠn_k-1]/Πn_k}}

Dark Matter Fraction Ω_DM = Ω_oY^{{[n-ΣΠn_k-1]/Πn_k}}{1-{(n-ΣΠn_k-1)/(n-ΣΠn_k-1+Πn_k)}³/{(n-ΣΠn_k-1)/(n-ΣΠn_k-1+Πn_k)}³ = Ω_oY^{{[n-ΣΠn_k-1]/Πn_k}}{(n-ΣΠn_k-1+Πn_k)³-(n-ΣΠn_k-1)³}/{n-ΣΠn_k-1}³
= Ω_oY^{{[n-ΣΠn_k-1]/Πn_k}}{(1+Πn_k/[n-ΣΠn_k-1])³ -1} = Ω_BM{(1+Πn_k/[n-ΣΠn_k-1])³ -1}

Dark Energy Fraction Ω_DE = 1- Ω_DM - Ω_BM = 1 - Ω_BM{(1+Πn_k/[n-ΣΠn_k-1])³}

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

Ω_oY^{{[n-ΣΠn_k-1]/Πn_k}} = ρ_BM+DMR_k(n)³/M_H = [N_k]³/[N_k+1]³ = {(n-ΣΠn_k-1)/(n-ΣΠn_k-1+Πn_k)}³ = R_k(n)³/V_H = V_dS/V_AdS
for ρ_BM+DM = M_H/R_H³ = ρ_critical and for Saturation at N_i = 6.541188... = constant ∀ N_i

(M_o/M_H).Y^{{[n-ΣΠn_k-1]/Πn_k}} = {(n-ΣΠn_k-1)/(n-ΣΠn_k-1+Πn_k)}³ with a Solution for f(n) in Newton-Raphson Root Iteration and first Approximation x₀

x_k+1 = x_k - f(n)/f'(n) = x_k - {(M_o/M_H).Y^{{[n-∑∏n_k-1]/Πn_k}} - (n-∑∏n_k-1)/(n-ΣΠn_k-1+Πn_k)³}/{(M_o/M_H).[lnY]Y^{{[n-ΣΠn_k-1]/Πn_k}} - 3(n-ΣΠn_k-1)²/(n-ΣΠn_k-1+Πn_k)⁴}

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


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




Baryon-Dark Matter Intersection:

N_k=√2 for n = √2.Πn_k + ΣΠn_k-1
n₀ = 1.√2 + 0 = n_o
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:

Y_k^{{(n-ΣΠn_k-1)/Πn_k}} = 2πΠn_k.R_H/λ_ps = Πn_k.R_H/r_ps = Πn_kM_H*^k/m_H*^k for M_H = c²R_H/2G_o and m_H = c²r_ps/2G_o

Hypermass M_Hyper = m_H.Y_k^{{(n-ΣΠn_k-1)/Πn_k}}

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

k=0 for M_Hyper = M_H = 1.M_H = m_H.Y^{(n)} with n = 1.{ln(2π/n_ps)/lnY} = n₁
= 234.472

k=1 for M_Hyper = n₁.M_H = M_H* = m_H.Y^{(n-1)/n₁} with n = [1] + n₁.{ln(2πn₁/n_ps)/lnY} = [1] + n₁n₂
= 1 + 234.472x245.812 = 57,637.03

k=2 for M_Hyper = n₁n₂.M_H = M_H** = m_H.Y^{{(n-1-n₁)/n₁n₂}} with n = [1 + n₁] + n₁n₂.{ln(2πn₁n₂/n_ps)/lnY} = [1 + n₁] + n₁n₂n₃
= 235.472 + 234.472x245.812x257.251 = 14,827,185.4

k=3 for M_Hyper = n₁n₂n₃.M_H = M_H*** = m_H.Y^{{(n-1-n₁-n₁n₂)/n₁n₂n₃}} with n = with n = [1 + n₁ + n₁n₂] + n₁n₂n₃.{ln(2πn₁n₂n₃/n_ps)/lnY} = [1 + n₁ + n₁n₂] + n₁n₂n₃n₄
= 57,871.74 + 234.472x245.812x257.251x268.785 = 3,985,817,947.8



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=H_ot for a nodal 'Hubble Constant' H_o=dn/dt as a function for a time dependent expansion parameter H(n)=H_o/T(n)=H_o/T(H_ot).

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 Λ_ps=Λ_QBB=G_oM_o/_λps² and where the wavelength of the de Broglie matter wave of the inflaton λ_ps 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.



3. Temperature Evolution in the Multiverse

In the early radiation dominated cosmology; the quintessence was positive and the matter energy dominated the intrinsic Milgröm deceleration from the Instanton n=n_ps 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 r_ps = λ_ps/2π, the critical modulated Schwarzschild radius r_ss = 2πλ_ss = 2πx10²² m* for λ_ps = 1/λ_ss
and for an applied scalefactor a = n/[n+1] =λ_ss/R_H = {1-1/[n+1]}

for a n=H_ot coordinate n_{recombination} = 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 n_ps.

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)=R_H(n/[n+1]) as the radius of the luminating surface
L(n_ps,T(n_ps) = 6π²λ_ps².σ.T_nps⁴ = 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) = 3H_oM_o.c²/550n and for Temperature T(n_ps) ----------- T(n_ps) = 2.93515511x10³⁶ Kelvin*.

T(n)⁴ = H_oM_oc²/(2π²σR_H²[550n³/[n+1]²]) for
T(n)⁴ = {[n+1]²/n³}H_oM_oc²/(2π²σR_H²[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(n_ps) 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(n_ps)=7.544808988..x10³⁷/2.93515511x10³⁶=25.705=1/0.03890...

​

Applying the actual VPE at the Instanton to this temperature gradient:

ρ_VPE/ρ_EMR = {4πE_ps/λ_ps³}/{8π⁵E_ps⁴/15h³c³} = 15/2π⁴ = 0.07599486.. = 1/12.9878.. indicating the proportionality E_VPE/E_EMR = kT_ps/kT_EMR = 2T_ps/T_potential at the Instanton from the Inflaton as a original form of the virial theorem, stating 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 M_o/2M_Hubble = r_Hyper/2R_Hubble Schwarzschild mass cosmo-evolution.

Now reducing the timeinstanton t_ps=n_ps/H_o 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 t_HiggsPE=t_ps.T(n_ps)/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 phase transition is the attunement of the BOSONIC UNIFICATION, namely the 'singularity' temperature T_ps=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 V_debroglie=c/n_ps of the Inflaton.



{(2-n)(n+1)}³/n³ = V_dS'/V_dS ......(4.36038 for n_present) in the first completing Hubble cycle
n³/(2-n)³ =V_AdS/V_dS' ................. (2.22379 for n_present) in the first completing Hubble cycle
(n+1)³ = VA_dS/V_dS .....................(9.69657 for n_present) in the first completing Hubble cycle

ρ_critical = 3H_o²/8πG_o {Sphere} and H_o²/4π²G_o {Hypersphere-Torus in factor 3π/2} (constant for all n per Hubble cycle)
ρ_critical = 3.78782x10^-27 [kg/m³]* and 8.038003x10^-28 [kg/m³]*


ρ_dSV_dS = ρ_dS'V_dS' = ρ_AdSV_AdS = ρ_criticalV_Hubble = M_Hubble = c²R_H/2G_o = 6.47061227x10⁵² kg*

​

https://cosmosdawn.net​

 

Inflation Curvature, Waved Matter and Hypermass

Describing the Einstein Lambda in the form of a parametrized Curvature Radius Λ(n)/R_Hubble= Λ(n)H_o/c = Λ(n)/R_H 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 M_o/2M_∞ =½Ω_BMps; with 'closure' mass M_∞=R_H.c²/2G_o=c³/2G_oH_o relates to the wormhole mass m_ps=hf_ps/c² =2.222..x10^-20 kg; as quantum eigenstate; the coupling between the Planck density ρ_P=l_P³/m_P=1.85x10⁹⁶ and the 'critical closure' density ρ_H=M_∞/R_H³ becomes subject to the overall mass evolution from the wormhole mass to the 'closure mass' over the evolution cycle, ending after for n_reset=234.5 for 3.96 Trillion years.

The coupling between the Planck Density and the Inflaton-Instanton Density so is: m_ps/R_H³ = hf_psc⁴/8G_o³M_H³ = 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 G_o 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: E_ps=E_{primary sourcesink}=hf_ps=m_psc² and the 'winding' and coupled self state is denoted by: E_ss=E_{secondary sinksource}=hf_ss=m_ssc²

The F-Space Unitary symmetry condition becomes: f_psf_ss=r_psr_ss=(λ_ps/2π)(2πλ_ss)=1

The coupling constants between the two eigenstates are so: E_psE_ss=h² and E_ps/E_ss=f_ps²=1/f_ss²
The Super-membrane E_psE_ss 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=f_ps² and the coupling constant for the winded low energy describes its MINIMISED reciprocal in df/dt|_min=f_ss².

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


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

Gravitational Fine structure (Electron): α_g = 2πG_om_e²/hc = {m_e/m_Planck}²

Gravitational Fine structure (Primordial Nucleon): α_n = 2πG_om_c²/hc

Gravitational Fine structure (Planck Boson): α_Planck = 2πG_om_Planck²/hc


1/E_ps=e*=2R_ec²=√{4αhce²/2πG_om_e²}=2e√α[m_P/m_e=2e√{α_e/α_g} = {2e²/m_e}√(k/G_o)=2e²/G_om_e = e²/2πε_om_e
for G_o = 1/k = 4πε_o for the cosmological unification of the fine structures.


E_ps = 1/E_ss = 1/e* = √{α_g/α_e}/2e = G_om_e/2e²

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

R_e 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: m_ec²=ke²/R_e; and for the electronic restmass m_e.
Alpha α is the electromagnetic fine structure coupling constant α=2πke²/hc for the electric charge quantum e, Planck's constant h and light speed constant c.
G_o is the Newtonian gravitational constant as applicable in the Planck-Mass m_P=√(hc/2πG_o).

Alternatively expressed, the mass seedling M_o of the QBB manifests in an emerging 'Black Hole' evolution and is bounded by the 'closure' mass M_∞=M_Hubble. 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 proto-stars 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 R_ylem = √{kTR_e³/G_om_c²}, R_e=e²/4πε_om_ec² and m_c 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 space-time into dS space-time.



" 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 Space-time 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 space-time parameters is resolved in a disengagement and an unnecessity of and for a prior existing space-time 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 point like singularity to a so called Planck string vibration formulated as the Planck length l_Planck and which can be considered to be a minimum 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 fine structure alpha {α=2πke²/hc} to the gravitational finestructure omega {ω = 2πG_om_Planck²/hc} via ke² = e²/4πε_o = G_oM_unification² for e² = {G_o/k}M_unification²
requiring dimensional mensuration identity in inflaton space [C²/Jm]=[Farad/meter] = [Jm/kg²] for [C] = [C*] = [Star-Charge Coulomb] = [m³/s²] = [VolumexAngular Acceleration] and for the Maxwell Constant 1/c² = μ_o.ε_o = {120π/c}{1/120πc} and 'Free Space' Inflaton Impedance Z_o= electric field strength E/magnetic field strength H = √(μ_o/ε_o) = cμ_o = 1/cε_o = 120π}.

Therefore,
[G_o]_mod =[4πε_o]_mod = [1/k]_mod and the inflaton dimensionless string modular unity is G_ok=1 for e² = G_o².M_unification² = M_unification²/k² and M_unification = 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 super-symmetry 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 m_c=m_Planck.α⁹ allows the breaking of the inflaton super-symmetry in the superstring classes.
Replacing the proto-nucleon mass m_c = √{hc/2πG_o}.{60πe²/h}⁹ = 9.924724523x 10^-28 kg by the effective electron mass m_e = ke²/2G_o(1.125x10¹²) =9.290527148x10^-31 kg sets the Electromagnetic Interaction/Gravitational Interaction ratio EMI/GI = e²/G_o²m_e² = {e/G_om_e}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 super-membrane 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 'macro quantum' radius R or a 'micro quantum' radius 1/R.

c = _λmin.f_max = 2πR_min.f_max as light speed invariance for the vibratory string mode R_curvature = R_min = λ_min /2π = Wormhole Perimeter/2π

1/c = 1/(λ_min.f_max) = λ_max.f_min = λ_max/f_max = R_max.f_min/2π as lightspeed invariance for the winding string mode R_curvature = R_max = 2π._λmax = 2π/Wormhole Perimeter

For the Harmonic Planck Energy Oscillator Energy E^o = ½hf_o = ½m_oc² = ½kT_Planck


Planck Mass = m_Planck = √{hc/2πG_o}
Planck Energy = E_Planck = m_Planck.c² = √{hc⁵/2πG_o} = hf_Planck = hc/l_Planck = kT_Planck
Planck Length =l_Planck = λ_Planck/2π = √{hG_o/2πc³}
Planck Temperature = T_Planck = E_Planck/k = √{hc⁵/2πk²G_o}
Planck Density = ρ_Planck= m_Planck/V_Planck = √{4π²c¹⁰/h²G_o⁴}/2π² = c⁵/πhG_o²= 9.40x10⁹⁴ kg/m³ for 9x10⁶⁰ permutation vibratory string eigenstates by |f_ps²|_mod.

Energy Density Inflaton/Energy Density Instanton = E_Planck.V_BigBang/E_BigBangV_Planck with minimum Inflaton Planck Oscillator: E^o_Planck = ½m_Planckc²
= m_Planck.r_wormhole³/m_wormhole.l_Planck³ = √{(hc/2πG_o)(2πc³/hG_o)}(2πc³/hG_o)(r_wormhole³/m_wormhole} = (c²/G_o)(2πc³/hG_o){r_wormhole³/m_wormhole}
= (2πc⁵/hG_o²){r_wormhole³/m_wormhole} = {4π²k²/h²G_o} (hc⁵/2πG_ok²){r_wormhole³/m_wormhole} = {kT_Planck}²(2πr_wormhole)²{1/h²G_o}{r_wormhole/m_wormhole}
= {E_Planck}².{c/hf_wormhole}².{1/G_o}}{r_wormhole/m_wormhole} = {E_Planck/E_BigBang}².{r_wormhole}{c²/G_om_wormhole} for the minimum Instanton Planck Oscillator: E^o_Planck = ½m_wormholec²

V_BigBang/V_Planck = {E_Planck/E_BigBang}.{r_wormhole}{c²/G_om_wormhole} for EV_BigBang/EV_Planck = EV_Instanton/EV_Inflaton = r_wormhole/R^o_wormhole = N_{Avagadro-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 mass content and its non-inertial 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 (M_i) 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 kinematic velocity as the ratio of displacement over time generalised in the light path X=cT}.

It is also well understood, that the inertial mass M_i 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 M_g is measured to be equivalent to the Inertial Mass M_i and is formulated in the 'Principle of Equivalence' in Einstein's Theory of General Relativity.
F-Theory then has shown, that this Inertial Mass M_i 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 Planck Quantum Law E=hf for light speed invariance c=λf)
(3) E=mc² iff f=f_o=f_ss (The Einstein Law E=mc² for the light speed upper limit)

(1) Whenever there is mass (M=M_i=M_g) occupying space; this mass can be assigned either as a photonic mass {by the Energy-Momentum relation of Special Relativity: E²=E_o²+(pc)²} by the photonic momentum p=h/λ=hf/c} OR a 'rest mass' m_o=m/√[1-(v/c)²] for 'rest energy' E_o=m_oc².

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 light speed 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 light speed c.

(3) If M>0, then there exists a mass-eigen frequency f_ss=f_o=E_ss/h=m_ssc²/h, which QUANTIZES all mass agglomerations m=Σm_ss in the mass quantum m_ss=E_ss/c².



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

https://youtu.be/-IfmgyXs7z8 https://youtu.be/tQSbms5MDvY
​

The Wave matter 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: λ_deBroglie = h/p = hc/pc for (pc) = √{E² - E_o²}= m_oc².√{[v/c]²/(1-[v/c]²)}

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


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

E_o = m_oc² with E = mc² = m_oc²/√{1-[v/c]²}, a 66.66% increase in the electron's energy describing the Kinetic Energy E - E_o = {m - m_o}c²
for a relativistic momentum p = m_oc.√{[0.8]²/(1-[0.8]²)} = (1.333..) m_oc = h/λ_deBroglie and for a relativistic de Broglie wavelength, 60% smaller, than for the non-relativistic electron in
λ_deBroglie = h/1.333..m_oc < h/0.8m_oc =λ_deBroglie (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 wave speed 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 'hyper accelerated' or tachyonic, the de Broglie wave speed being lower bounded by light speed 'c'

v_phase = wavelength.frequency = (h/mv_group)(mc²/h) = c²/v_group > c for all v_group < c

m = Energy/c² = hf/c² = hc/λ_deBrogliec² = h/λ_deBrogliec = m_deBroglie = [Action as Charge²]_mod/c(Planck-Length Oscillation)
= [e²]_mod/cl_Planck√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 2R_e = e*/c² = [ec]_modular as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy quantum E_ps=hf_ps=m_psc²=kT_ps as a function of e*=1/E_ps of Heterotic superstring class HE 8x8 and relating the Classical Electron Diameter {2R_e} as Monopole Mass [ec]_mod in Curvature Radius r_ps=λ_ps/2π = G_om_ps/c².

The factor 2G_o/c² multiplied by the factor 4π becomes Einstein's Constant k = 8πG_o/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 2R_e/30[ec]_mod = 2R_ec²/30[ec³]_mod = e*/30[ec³]_mod ∝ κ for a proportionality constant {κ*}=2R_e/30k[ec]_mod = 2R_e.c²/8πe = e*/8πe =1.2384..x10²⁰ kg*/m* in string units for Star Charge in Star Colomb C*/Electro Charge 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 m_psc²c/[ec]_modular = [c³]_modular = 2.7x10²⁵ electron volt or 4.3362x10⁶ J for a monopole mass [ec]_modular = m_monopole = 4.818x10^-11 kg* .

Mass M = n.m_ss = Σm_ss = n.{h/2πr_deBrogliec} .[E_ss.e*]_mod = n.m_ps.[E_ss.{9x10⁶⁰}.2π²R_rmp³]_mod = n.m_ps.[E_ss.{2R_e.c²}]_mod = n.[E_ps.E_ss]_mod.[2R_e]_mod
for λ_deBroglie=λ_ps=h/m_psc and [E_ps.e*]_mod =1

{2R_ec²} = 4G_oM_Hyper for the classical electron radius R_e=ke²/m_ec² and describes its Hyper-Mass M_{Hyper-electron} = R_ec²/2G_o = ke²/2G_om_e = 1.125x10¹² kg* for an effective electron mass of m_e = ke²/2G_o(1.125x10¹²) =9.290527148x10^-31 kg* in string units and where k=1/4πε_o = 9x10⁹ (Nm²/C²)*.

The curvature radius for the electron mass m_e = r_electronc²/2G_o then becomes r_electron = 2G_om_e/c² = 2.293957...x10^-57 m* in string-membrane inflaton space as 1.44133588x10^-34 r_ps in the wormhole instanton space.

R_e/r_{inflaton-electron} = M_{Hyper-electron}/m_e = 1.2109108..x10⁴² = ½(EMI/GI) = ½(e²/G_o²m_e²) =½ {e/G_om_e}² = ½(2.421821677x10⁴² ) for the classical electron radius R_e halved from the classical electron diameter 2R_e from the definition for the modulated supermembrane coupled in E_psE_ss=h² and E_ps/E_ss=f_ps²=1/f_ss².

Mass M = n.m_ss = Σm_ss = n.{m_ps} .[E_ss.e*]_mod = n.{m_ps}[{hf_ss}{f_ps/f_ss}.2π²R_rmp³]_mod = n.m_ps.[E_ps.e*/f_ss²]_mod = n.m_ps/|f_ss²|_mod



Hyper-Mass and the Hawking Modulus in Curvature of Space-time

A general solution for the Curvature Radius R_Curvature 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: ------------R_Curvature = 2G_oM/c²
for Hyper-Mass:----------------M_Hyper = hc³.e*/4πG_o = ½N_{Avagadro-Instanton}.m_wormhole

Hyper-Mass M_Hyper 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 r_wormhole=r_ps=r_min 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 r_min = 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 E^o_BigBang=½m_psc²=½hf_ps=½kT_ps=½E_ps=1/2e*

M_Hyper/½m_ps = 2hc³.e*/4πG_o.m_ps = N_{Avagadro-Instanton} = r_ps/R_ps
N_{Avagadro-Instanton} = 5.8012x10²³ for hypermass
M_Hyper = hc³.e*/4πG_o = ½N_{Avagadro-Instanton}.m_wormhole
for R_ps = G_om_ps/c² = r_ps/N_{Avagadro-Instanton} = 2.743...x10^-47 m* in Inflaton membrane space of 11D and string space of 10D

M_Hyper/m_min = M_min/m_min = {n.hc³e*/4πG_o}/m_min = {n.r_minc²/2G_o}/m_min = {hc³.c²/4πG_oE_min}{ne*} = {hc³.c²/4πG_ohf_min}{ne*} = {2πr_min.hc³.c²/4πG_ohc}{ne*} = {r_min.c².E/2G_oM}{ne*} = r_min/R.{Ene*} for R = 2G_oM/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.λ_min.

m_Hyper/r_min = {r_minc²/2G_o}/r_min = c²/2G_o = n.m_min.Ee*/R = M/R_curv for de Broglie wave matter m_min = hf_min/c² = h/cλ_min

Utility of the Schwarzschild metric allows calculation of Black Hole matter equivalents for any mass M>r_minc²/2G_o say for a planetary mass M_Earth = 6x10²⁴ kg for a
r_curv = 0.015 meters and for a solar mass M_Sun = 2x10³⁰ kg* for a r_curv = 4938.3 meters*.

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

For any mass M<r_minc²/2G_o 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 t_min=t_ps=1/f_ps=[f_ss]_mod

The Standard Gravitational Parameter μ= GM = constant = G_oM(XⁿYⁿ)= G_oXⁿ.MYⁿ and for (XY)ⁿ=1 can be finestructured in a decreasing gravitational constant G(n)=G_oXⁿ with a corresponding increase in the mass parameter M as M(n)=M_oYⁿ as say for the proto-nucleonic mass of the Instanton m_c(n_ps) as m_c(n_present) = m_c.Y^n_present = m_neutron < m_cY^n_present = 1.711752..x10^-27 kg* and 958.99 MeV* upper limited

For a changing Gravitational constant G(n_present) .m_neutron(n_present)² = G_om_c².Y^n_present and is modulated say in A micro-macro Black Hole perturbation M_o²/2M_∞.M_MaxHawking = 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 = m_Planck.E^o_Planck/k = √{hc/2πG_o}{½m_Planck.c²/k} = hc³/4πG_ok = {M_Smin.T_Smax} = {m_ps.T_ps.½N_{Avagadro-Instanton}} =
[c²/4π²]_mod.{M_MaxHawking .T_Smin } = 9.131793821x10²³ kg*K* with (m_psT_ps = E_ps²/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 M_min.T_max = hc³/4πG_ok = [c²/4π²]_mod.M_max.T_min = ½m_Planck.T_Planck = M_MaxHawking. [c²/4π²]_mod.T_ss and the Hawking Mass is determined as M_MaxHawking = λ_maxπc²/G_o = 2.54469..x10⁴⁹ kg*.

Hyper-Mass M_Hyper (n_ps) = hc³.e*/4πG_o = ½N_{Avagadro-Instanton}.m_wormhole = 6445.775 kg at the Instanton boundary n=n_ps so increases to M_Hyper(n_present)Y^n_present =hc³.e*/4πG_oX^n_present ~ 11,117.26 kg as the projected Instanton boundary mass for the wormhole radius r_wormhole = r_ps = N_{Avagadro-Instanton}.R_ps modulating the Inflaton curvature with the Instanton curvature and utilizing n_present=1.1327... for a decreased perturbed G(n_present) = 6.442x10^-11 G-string units for the Standard Gravitational Parameter G(n)m_iY^k(n).m_jY^n-k = G_om_c² = constant for G(n)=G_oXⁿ.

Using the λ_minλ_max=1 wavelength modulation in the T-duality of λ_min=2πR_min=1/λ_max=2π/R_max, we can see, that this modulation closely approximates the geometric mean of the seedling mass in {1/4π}M_o²/2M_∞.M_Max=M_o²/8π.M_∞.M_Hawking=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 G_m(n)=G_o.and apply our just derived Black Hole Mass modulation coupled to that of the quantum micromasses.

We had: G_om_c²={G_oX^n+k}.{m_cYⁿ}.{m_cY^k}=G_m(n).m_nmax.m_nmin and where G_m is the actual G value as measured and which has proved difficult to do so in the laboratories.
G_m(n)=G_o.X^n+k=G_om_c²/m_nmax.m_nmin=G_om_c²/({m_cYⁿ}{m_nmin}) and where we have m_nmin=m_cY^k} for the unknown value of k with m_nmax=m_cYⁿ.

So G_m(n)=G_o.X^n+k=G_oXⁿ[m_c/m_nmin]=G_o{m_c²/m_cYⁿ}.{M_o²/8π.M_∞.M_Hawking.m_av} for X^k={m_c/m_av}.{M_o²/8π.M_∞.M_Hawking}=1.00109044..{m_c/m_av}
and where now {m_nmin}={8π.M_∞.M_Hawking.m_av/M_o²}=1.00109044..m_av.
m_av={M_o²/8π.M_∞.M_Hawking}{m_nmin}={M_o²/8π.M_∞.M_Hawking}{m_cY^k}=0.9989107..{m_cY^k} and obviously represents a REDUCED minimum mass m_nmin=m_cY^k.

But the product of maximum and 'new' minimum now allows an actual finetuning to a MEASURED nucleon mass m_N by:
m_N² = m_avYⁿ.m_cYⁿ=m_av.m_nmax.Yⁿ.

So substituting for m_av in our G_m expression, will now give the formulation:
G_m(n)=G_o.X^n+k=G_oXⁿ[m_c/m_nmin]=G_o{m_c²/m_cYⁿ}.{M_o²/8π.M_∞.M_Hawking.m_av}
G_m(n)=G_o.X^n+k=G_oXⁿ[m_c/m_nmin]=G_o{m_c²/m_cYⁿ}.{M_o²/8π.M_∞.M_Hawking}{m_cY²ⁿ/m_N²}
G_m(n)=G_o.{m_c²/m_N²}{M_o²/8π.M_∞.M_Hawking}Yⁿ

The average nucleon mass m_N 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: m_neutron=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(n_p)= G_o{m_c/m_neutron}².(0.9989107..)Y^n_p = 6.670693x10^-11 (m³/kgs²)* or 6.675312x10^-11 (m³/kgs²).

For a Proton Restmass of: m_proton=1.6788956x10^-27 kg* (940.5833 MeV*) or (1.672618x10^-27 kg and 938.270 MeV).
G(n_p) = G_o{m_c/m_N}².(0.9989107..)Y^n_p = 6.6895399x10^-11 (m³/kgs²)* or 6.694171x10^-11 (m³/kgs²).

G_m(n)=G_o.X^n+k = 6.670693x10^-11 (m³/kgs²)* then gives k_p =ln{G_m(n_p)/G_o}/ln{X} - n_p = 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 m_c.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 m_c=√Omega.m_P=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 m_p=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
Neutron m_n=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 G_mYⁿ/G_o ~ 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 X^n+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 e^u=1+u+u²/2!+u³/3!+u⁴/4!+...

For a function f(n)=z=G_m(n)/G_o=X^n+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=n_ps=λ_ps/R_max=6.2591x10^-49 ~ 0
Then G_BigBang=G_oX^n_ps=G_o (to 50 decimal places distinguishing the timeinstanton from the Nulltime as the Planck-Time transform).
G_o 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(G_mYⁿ/G_o)/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 n_present=H_ot_present=1.132711...

The introduction of the mass seed coupling between the macro quantum M_o and the micro quantum m_c=m_Palpha⁹ (from the gravitational finestructure unification) PERTURBS the 'purely electromagnetic' cosmology in the perturbation factor k and increases the purely electromagnetic G_memr 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)/R_max={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 q_o=½Ω_o=M_o/2M_∞=2G_oH_oM_o/c³ ~0.014015... This open universe is bounded in the 'standing wave' of the Hubble Oscillation of the 11D and 'higher dimensional universe'.
​

 

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 ΩDM=ΩBMx [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 -P0=Λ0c2/4πGoR0 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=hRH/λpsc2 =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
n(tGenesis)= nFalseVacuum= ∛{{Ho3Mo/1100π2σ}{npsk/h}4} = 8.252x10-51 De Broglie Matter Wave Inflaton Quantum Oscillation	8.252x10-51	-	tGenesis=nGenesis/Ho = 4.395x10-33 s*	T(nGenesis) =∜{{Ho3Mo/1100π2σ}.{(nGenesis+1)2/nGenesis3}} = 7.5448x1037 K* in the Higgs false vacuum and {npsk/h}|mod.	RH=1.5977x1026	-	-	vdB=RHfps 4.7930x1056 adB=RHfps2 1.4379x1087	E=hF=kT=Mc2	-	M=hRH/λpsc2 =0.0118346323 (33/20)12mcNAv
n(tdBmin) = 8.772x10-51	8.772x10-51	-	tdBmin= qotps = ndBmin/Ho = nps{GoMo/c3}= 4.672x10-33 s*	T(ndBmin)=∜{{Ho3Mo/1100π2σ}.{(ndBmin+1)2/ndBmin3}} = 7.206x1037 K* in the Higgs false vacuum from the DE gradient instanton bounce for deceleration parameter qo=Λo/AdB	RH=1.5977x1026	-	-	vdB=RHfps 4.7930x1056 adB=RHfps2 1.4379x1087	E=hF=kT=Mc2	-	M=hRH/λpsc2 =0.0118346323 (33/20)12mcNAv
n(tdBmin) = 1.754x10-50	1.754x10-50	-	2tdBmin= Ωotps = 2ndBmin/Ho = nps{2GoMo/c3}= 9.343x10-33 s*	T(ndBmin)=∜{{Ho3Mo/1100π2σ}.{(ndBmin+1)2/ndBmin3}} = 4.285x1037 K* in the Higgs false vacuum from the DE gradient instanton bounce for Ωo=Mo/MH	RH=1.5977x1026	-	-	vdB=RHfps 4.7930x1056 adB=RHfps2 1.4379x1087	E=hF=kT=Mc2	-	M=hRH/λpsc2 =0.0118346323 (33/20)12mcNAv
n(tHPFV) = 2.435x10-50	2.435x10-50	-	tHPFV={T(nps)/TEMPERATURE}tps =nHPFV/Ho = 1.297x10-32 s*	T(nHPFV) =∜{{Ho3Mo/1100π2σ}.{(nHPFV+1)2/nHPFV3}} = 3.351x1037 K* in the Higgs false vacuum	RH=1.5977x1026	-	-	vdB=RHfps 4.7930x1056 adB=RHfps2 1.4379x1087	E=hF=kT=Mc2	-	M=hRH/λpsc2 =0.0118346323 (33/20)12mcNAv
n(tdBmax) =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	T(ndBmax) =∜{{Ho3Mo/1100π2σ}.{(ndBmax+1)2/ndBmax3}} =1.857x1037 K* in the Higgs false vacuum from the Planck-Stoney inflaton time bounce	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 nps=λps/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= GoMo/λps2-2cHo =2.01522x1085 Λo/Ro= GoMo/λps3 -2Ho2RH/λps =GoMo/λps3 -2Hofps =2.01522x10107 -P=Λoc2/4πGoRo =1.2990x10133 n≥nps	mH=6445.7752 mps=2.222x10-20 Yn=2πRH/λps =MH/mH
n=3.562x10-27 Bosonic Unification	3.562x10-27	1.68x1013	1.897x10-9 s*	hfps/k= 1.417x1020	0.569092	H=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	5.145x10-21	1.39x1010	0.00274 s*	3.400x1015	822,004.02	H=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 RG=λps∛{G}/2π =3.391558x1011 m*	2.1228x10-15	2.170x107	1130.515 s* Meson VPE Inner Primordial Neutron Decay	2.089x1011	3.39156x1011 - - 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 RF=λps∛{F}/2π =3.4510775x1011m*	2.1601x10-15	2.152x107	1150.380 s* Meson VPE Outer Primordial Neutron Decay	2.061x1011	3.45108x1011 - - 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 RE=λps∛{E}/2π =3.4359711x1014 m*	2.1506x10-12	681,835	1,145,320.3 13d6h8m 40.3s*	1.163x109	3.43597x1014 - - 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	2.30x10-5	293.9	388,141.5 y	2945	3.6746x1021 - -	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	6.30x10-5	177.2	1.0632 My	2935	λss=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=0.000393425	3.93x10-4	49.421	6.6395 My	739.53	2πx1022 - -	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 adB/ΛBM=Mo/2MH RSarkar =GoMo/c2	0.01382	7.478	236.5186 My	51.062	2.2391x1024 - -	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	0.02727	5.015	473.0373 My	30.571	4.3562x1024 - -	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	0.05338	3.272	0.9517 Gy	18.335	8.5285x1024 - -	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	0.09766	2.125	1.8265 Gy	11.523	1.5603x1025 - -	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	0.11716	1.840	2.2396 Gy	9.9976	1.8712x1025 - -	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	0.19283	1.177	4.0317 Gy	6.7278	3.0803x1025 - -	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	0.33333	0.612	8.4381 Gy	4.2544	5.3256x1025 - -	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	0.36940	0.523	9.8860 Gy	3.8845	5.9019x1025 - -	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=0.618034	0.38197	0.495	10.4300 Gy	3.7692	6.1026x1025 - -	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	0.3432	14.6365 Gy	3.1405	7.4206x1025 - -	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	0.2910	to=t-tps=1/Ho 16.8761 Gy	2.9210	8.4837x1025 1.5977x1026 3.1954x1026	H=½ Ho=29.02 H'=Ho/n=58.04 -1.8750 Ho2 -1.0000 Ho2	-½ 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] =λps=10-22 R1E=[n-1]RH =λps =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 ΩDM=ΩBM.{[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 =GoMo/λps2 -2cHo/n1 =2.01522x1085 Λ1/R1= GoMo/R13 -2Ho2n1/[n-1] [n-1+n1]2 GoMo/λps3 -2Hofps/n1 =2.01522x10107 -P1=Λ1c2/4πGoR1 =1.2990x10133 n≥1+nps	HyperMass MHyper= mHY{[n-1]/n1} MH*=n1MH =1.51717x1055 mps=2.22x10-20 Y{[n-1]/n1} =2πn1RH/λps =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↩ Xn=ΩBMo 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] =λps=10-22 R2E=[n-1-n1]RH =λps R2P= [n-1-n1+n1n2]R2E =[n1n2]λps =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 ΩDM=ΩBM.{[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 =GoMo/λps2 -2cHo/n1n2 =2.01522x1085 Λ2/R2=GoMo/R23 -2Ho2n1n2/ [n-1-n1] [n-1-n1+n1n2]2 =GoMo/λps3 -2Hofps/n1n2 =2.01522x10107 -P2=Λ2c2/4πGoR2 =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} =2πn1n2RH/λps =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 -½ 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] =λps=10-22 R3E=[n-1-n1 -n1n2]RH =λps R3P=[n-1-n1- n1n2+ n1n2n3]R3E =[n1n2n3]λps =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 ΩDM=ΩBM.{[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 =GoMo/λps3-2cHo/n1n2n3 =2.01522x1085 Λ3/R3=GoMo/R33 -2Ho2n1n2n3/ [n-1-n1-n1n2] [n-1-n1-n1n2+n1n2n3]2 =GoMo/λps3 -2Hofps/n1n2n3 =2.01522x10107 -P3=Λ3c2/4πGoR3 =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}= 2πn1n2n3RH/λps =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 4.8671x1027	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/n1n2 =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 -½ 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