**Cosmogenesis – A Story of Creation in Membrane Mirror Symmetry**

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

**Abstract:**

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

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.

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

^{-31}s; 16.88 Gy; 3.96 Ty} and the second universe, timeshifted in t

_{1}=t

_{o}+t with t

_{o}=1/H

_{o}has a nodal configuration {t

_{o}+1.4×10

^{-33}; t

_{o}+3,957 Gy; t

_{o}+972.7 Ty}; the latter emerging from the timespace as the instanton at time marker t

_{o}. A third universe would initiate at a time coordinate t

_{2}=t

_{o}+t

_{1}+t as {1/H

_{o}+234.472/H

_{o}+5.8×10

^{-36}s; t

_{o}+t

_{1}+972.7 Ty; t

_{o}+t

_{1}+250,223 Ty}; but as the second node in the second universe cannot be activated by the lightpath until the first universe has reached its 3.96 trillion year marker (and at a time for a supposed ‘heat death’ of the first universe due to exhaustion of the nuclear matter sources); the third and following nested universes cannot be activated until the first universe reaches its n=1+234.472=235.472 timespace coordinate at 3,974.8 billion years from the time instanton aka the Quantum Big Bang.

For a present timespace coordinate of n_{present}=1.13242 however; all information in the first universe is being mirrored by the timespace of the AdS spacetime into the dS spacetime of the second universe at a time frame of t = t_{1}-t_{o} = 19.11 – 16.88 = 2.23 billion years and a multidimensional time interval characterizing the apparent acceleration observed and measured in the first universe of the Calabi Yau manifold compressed or compactified flat dS Minkowski cosmology. The solution to the Dark Energy and Dark Matter question of a ‘missing mass’ cosmology is described in this discourse and rests on the evolution of a multiverse in matter.

**Y ^{n} = R_{Hubble}/r_{Weyl} = 2pR_{Hubble}/l_{Weyl }= w_{Weyl}/H_{o} = 2pn_{Weyl } = n_{ps}/2p = 1.003849×10^{49}**

_{Hubble(1)}= n

_{1}R

_{Hubble}= c/H

_{o(1)}= (234.472)R

_{Hubble}= 3.746×10

^{28}m* in 3.957 Trillion Years for critical n

_{k}3rd Inflaton/Quantum Big Bang

_{Hubble(2)}= n

_{1}n

_{2}R

_{Hubble}= c/H

_{o(2)}= (234.472)(245.813)R

_{Hubble}= 9.208×10

^{30}m* in 972.63 Trillion Years for critical n

_{k}4th Inflaton/Quantum Big Bang

_{Hubble(3)}= n

_{1}n

_{2}n

_{3}R

_{Hubble}= c/H

_{o(3)}= (57,636.27)(257.252)R

_{Hubble}= 2.369×10

^{33}m* in 250.24 Quadrillion Years for critical n

_{k}5th Inflaton/Quantum Big Bang

_{Hubble(4)}= n

_{1}n

_{2}n

_{3}n

_{4}R

_{Hubble}= c/H

_{o(4)}= (14,827,044.63)(268.785)R

_{Hubble}= 6.367×10

^{35}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}P n_{k}= c/H_{o}P n_{k}**n**

_{k}= ln{w_{Weyl}R_{Hubble(k)}/c}/lnY = ln{w_{Weyl}/H_{o(k)}}/lnY**L**

_{k}(n) = G_{o}M_{o}/R_{k}(n)^{2}– 2cH_{o}(Pn_{k})^{2}/{n-SPn_{k-1}+Pn_{k})^{3}}_{o}M

_{o}(n-SPn

_{k-1}+Pn

_{k})

^{2}/{(Pn

_{k})

^{2}.R

_{H}

^{2}(n-SPn

_{k-1})

^{2}} – 2cH

_{o}(Pn

_{k})

^{2}/{n-SPn

_{k-1}+Pn

_{k})

^{3}}

_{o}= G

_{o}M

_{o}(n+1)

^{2}/R

_{H}

^{2}(n)

^{2}– 2cH

_{o}/(n+1)

^{3}L

_{1}= G

_{o}M

_{o}(n-1+n

_{1})

^{2}/n

_{1}

^{2}R

_{H}

^{2}(n-1)

^{2}– 2cH

_{o}n

_{1}

^{2}/(n-1+n

_{1})

^{3}L

_{2}= G

_{o}M

_{o}(n-1-n

_{1}+n

_{1}n

_{2})

^{2}/n

_{1}

^{2}n

_{2}

^{2}R

_{H}

^{2}(n-1-n

_{1})

^{2}– 2cH

_{o}n

_{1}

^{2}n

_{2}

^{2}/(n-1-n

_{1}+n

_{1}n

_{2})

^{3}…..

_{k}=1=n

_{o}and Pn

_{k-1}=0 for k=0 with Instanton/Inflaton resetting for initial boundary parameters

_{o}/a

_{deBroglie}= G

_{o}M

_{o}/R

_{k}(n)

^{2}/Pn

_{k}R

_{H}f

_{ps}

^{2}= {G

_{o}M

_{o}(n-SPn

_{k-1}+Pn

_{k})

^{2}/{[Pn

_{k}]

^{2}.R

_{H}

^{2}(n-SPn

_{k-1})

^{2}(Pn

_{k}R

_{H}f

_{ps}

^{2})} = (Pn

_{k})½W

_{o }

_{o}= M

_{o}*/M

_{H}* = 0.02803 for the kth universal matter evolution

_{ps}=H

_{o}t and L

_{o}/a

_{deBroglie}= G

_{o}M

_{o}(n

_{ps}+1)

^{2}/{R

_{H}

^{3}n

_{ps}

^{2}(f

_{ps}

^{2})} = G

_{o}M

_{o}/R

_{H}c

^{2}= M

_{o}/2M

_{H}= ½W

_{o}k=1 for Reset

_{ps}and L

_{o}/a

_{deBroglie}= G

_{o}M

_{o}(1+n

_{ps}-1+n

_{1})

^{2}/{[n

_{1}]

^{2}.R

_{H}

^{3}(1+n

_{ps}-1)

^{2}(n

_{1}f

_{ps}

^{2})} = M

_{o}/2n

_{1}M

_{H}= M

_{o}/2M

_{H}* = ½W

_{o}* k=2 for Reset

_{1}+1+n

_{ps}and L

_{o}/a

_{deBroglie}= G

_{o}M

_{o}(n

_{1}+1+n

_{ps}-1-n

_{1}+n

_{1}n

_{2})

^{2}/{[n

_{1}n

_{2}]

^{2}.R

_{H}

^{3}(n

_{1}+1+n

_{ps}-1-n

_{1})

^{2}(n

_{1}n

_{2}f

_{ps}

^{2})} = ½W

_{o}** k=3 for Reset

_{1}n

_{2}+n

_{1}+1+n

_{ps}and L

_{o}/a

_{deBroglie}= G

_{o}M

_{o}(n

_{1}n

_{2}+n

_{1}+1+n

_{ps}-1-n

_{1}-n

_{1}n

_{2}+n

_{1}n

_{2}n

_{3})

^{2}/{[n

_{1}n

_{2}n

_{3}]

^{2}.R

_{H}

^{3}(n

_{1}n

_{2}+n

_{1}+1+n

_{ps}-1-n

_{1}-n

_{1}n

_{2})

^{2}(n

_{1}n

_{2}n

_{3}f

_{ps}

^{2})} = ½W

_{o}*** ……

_{ps }= 2pP

_{nk-1}.X

^{nk}= l

_{ps}/R

_{H}= H

_{o}t

_{ps}= H

_{o}/f

_{ps}= ct

_{ps}/R

_{H}and R

_{H}=2G

_{o}M

_{H}/c

^{2}

_{o}=H

_{o}t

_{o}/n

_{o}=H

_{o}t=n N

_{1}=H

_{o}t

_{1}/n

_{1}=(n-1)/n

_{1}N

_{2}=H

_{o}t

_{2}/n

_{1}n

_{2}=(n-1-n

_{1})/n

_{1}n

_{2}N

_{3}=H

_{o}t

_{3}/n

_{1}n

_{2}n

_{3}=(n-1-n

_{1}-n

_{1}n

_{2})/n

_{1}n

_{2}n

_{3}…. dn/dt=H

_{o}…..

N

_{k}=H

_{o}t

_{k}/Pn

_{k}=(n-SPn

_{k-1})/Pn

_{k}t

_{k}= t – (1/H

_{o})SPn

_{k-1}for n

_{o}=1 and N

_{o}=n

_{o}=t=n/H

_{o}=N

_{o}/H

_{o}=nR

_{H}/c t

_{1}=t-1/H

_{o}=(n-1)/H

_{o}=[n

_{1}N

_{1}]/H

_{o}t

_{2}=t-(1+n

_{1})/H

_{o}=(n-1-n

_{1})/H

_{o}=(n

_{1}n

_{2}N

_{2})/H

_{o}t

_{3}=t-(1+n

_{1}+n

_{1}n

_{2})/H

_{o}=(n-1-n

_{1}-n

_{1}n

_{2})/H

_{o}=(n

_{1}n

_{2}n

_{3}N

_{3})/H

_{o}…….

_{o})=n

_{o}R

_{H}{n/[n+1]}=R

_{H}{n/[n+1]} R

_{1}(N

_{1})=n

_{1}R

_{H}{N

_{1}/[N

_{1}+1]}=n

_{1}R

_{H}{[n-1]/[n-1+n

_{1}]} R

_{2}(N

_{2})=n

_{1}n

_{2}R

_{H}{N

_{2}/[N

_{2}+1]}=n

_{1}n

_{2}R

_{H}{[n-1-n

_{1}]/[n-1-n

_{1}+n

_{1}n

_{2}]} R

_{3}(N

_{3})=n

_{1}n

_{2}n

_{3}R

_{H}{N

_{3}/[N

_{3}+1]}=n

_{1}n

_{2}n

_{3}R

_{H}{[n-1-n

_{1}-n

_{1}n

_{2}]/[n-1-n

_{1}-n

_{1}n

_{2}+n

_{1}n

_{2}n

_{3}]} …….

**R**

_{k}(n) = Pn_{k}R_{H}(n-SPn_{k-1})/{n-SPn_{k-1}+Pn_{k}}_{H}(n/[n+1]) = n

_{1}R

_{H}(N

_{1}/[N

_{1}+1]) = n

_{1}n

_{2}R

_{H}(N

_{2}/[N

_{2}+1]) =….

**V _{k}(n) = dR_{k}(n)/dt = c{Pn_{k}}^{2}/{n-SPn_{k-1}+Pn_{k}}^{2}**

…..= c/[n+1]

^{2}= c/[N

_{1}+1]

^{2}= c/[N

_{2}+1]

^{2}=….. …..= c/[n+1]

^{2}= c(n

_{1})

^{2}/[n-1+n

_{1}]

^{2}= c(n

_{1}n

_{2})

^{2}/[n-1-n

_{1}+n

_{1}

^{2}n

_{2}

^{2}]

^{2}=…..

**A _{k}(n) = d^{2}R_{k}(n)/dt^{2} = -2cH_{o}(Pn_{k})^{2}/(n-SPn_{k-1}+Pn_{k})^{3}**

…..= -2cH_{o}/(n+1)^{3} = -2cH_{o}/n_{1}(N_{1}+1)^{3} = -2cH_{o}/n_{1}n_{2}(N_{2}+1)^{3}=….. ….. = -2cH_{o}/[n+1]^{3} = -2cH_{o}{n_{1}}^{2}/[n-1+n_{1}]^{3} = -2cH_{o}(n_{1}n_{2})^{2}/[n-1-n_{1}+n_{1}n_{2}]^{3} =…..

G_{o}M_{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

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_{o}t 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_{o}t).

It is found, that the Dark Matter (DM) component of the universe evolves as a function of a density parameter for the coupling between the inflaton of AdS and the instanton of dS space times. It then is the coupling strength between the inflationary AdS brane epoch and the QBB dS boundary condition, which determines the time evolution of the Dark Energy (DE). Parametrization of the expansion parameter H(n) then allows the cosmological constant term in the Friedmann equation to be merged with the scalar curvature term to effectively set an intrinsic density parameter at time instantenuity equal to L(n) for L_{ps}=L_{QBB}=G_{o}M_{o}/l_{ps}^{2} and where the wavelength of the de Broglie matter wave of the inflaton l_{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.

**dH/dt + 4pGr = – 4pGP/c**

^{2}_{4/10D}=[4p/3]R

_{H}

^{3}and V

_{5/11D}=2p

^{2}R

_{H}

^{3}in factor 3p/2)

For Hypersphere Volumar of 3-sphere: d

^{2}{V

_{4}}/dR

^{2}= d

^{2}{½p

^{2}R

^{4}}/dR

^{2}= d{2p

^{2}R

^{3}}/dR = 6p

^{2}R

^{2}Surface Area of Horn Torus (2pR)(2pR)= 4p

^{2}R

^{2}

_{ps}= 2pr

_{ps}= n

_{ps}R

_{H}= c/f

_{ps}= H

_{o}R

_{H}/f

_{ps}

4pM

_{o}/R

^{3}= M

_{o}/{2p2(l

_{ps}/2p)

^{3}} = M

_{o}/{4p

^{2}{l

_{ps}/2p}

^{3}for E

_{ps}ZPE/VPE density 4pE

_{ps}/r

_{ps}

^{3}

{4pM

_{o}/R

^{3}}.{3p/2} = 3M

_{o}/{4p(l

_{ps}/2p)

^{3}} = 6p

^{2}M

_{o}/l

_{ps}

^{3}= 4p.{3p/2}M

_{o}/l

_{ps}

^{3}= 4p.d

_{Feigenbaum chaos limit }{M

_{o}/l

_{ps}

^{3}}

_{reset}= R

_{k}(n)

_{AdS}/R

_{k}(n)

_{dS}+ ½ = n-SPn

_{k-1}+Pn

_{k}+½ Scalefactor modulation at N

_{k }= {[n-SPn

_{k-1}]/Pn

_{k}} = ½ reset coordinate

{dH/dt} = a

_{reset}.d{H

_{o}/T(n)}/dt = – H

_{o}

^{2}(2n+1)(n+3/2)/T(n)

^{2 }for k=0

**dH/dt + 4pGr = – 4pGP/c**

^{2}_{o}

^{2}(2n+1)(n+3/2)/T(n)

^{2}+ G

_{o}M

_{o}/{R

_{H}

^{3}(n/[n+1])

^{3}}{4p} = L(n)/{R

_{H}(n/[n+1])} + L/3 -2H

_{o}

^{2}{[n+1]

^{2}-¼}/T[n]

^{2}+ G

_{o}M

_{o}/R

_{H}

^{3}(n/[n+1])

^{3}{4p} = L(n)/R

_{H}(n/[n+1]) + L/3 -2H

_{o}

^{2}{[n+1]

^{2}-¼}/T(n)

^{2}+ 4p.G

_{o}M

_{o}/R

_{H}

^{3}(n/[n+1])

^{3}= L(n)/R

_{H}(n/[n+1]) + L/3

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

**Λ(n)/R**

_{H}(n/[n+1]) = – 4πGP/c^{2}= G_{o}M_{o}/R_{H}^{3}(n/[n+1**])**

^{3}-2H_{o}^{2}/(n[n+1]^{2})^{2}[n+1]/4πG

_{o}nR

_{H}=Λ(n)H

_{o}c[n+1]/4πG

_{o}n = M

_{o}c

^{2}[n+1]

^{3}/4πn

^{3}R

_{H}

^{3}– H

_{o}

^{2}c

^{2}/2πG

_{o}n[n+1]

^{2}

^{-11 }J/m

^{3})* = (2.12682×10

^{-11 }J/m

^{3})* + (-8.82709×10

^{-11 }J/m

^{3})* 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}=-0.5585, the DE Lambda calculates as -6.700×10^{-11} (N/m^{2}=J/m^{3})*, albeit as a positive pressure within the negative quintessence.

In the early radiation dominated cosmology; the quintessence was positive and the matter energy dominated the intrinsic Milgröm deceleration from the Instanton n=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 }= l_{ps}/2p, the critical modulated Schwarzschild radius r_{ss }= 2pl_{ss} = 2px10^{22} m* for l_{ps} = 1/l_{ss} and for an applied scalefactor a = n/[n+1] = l_{ss}/R_{H} = {1-1/[n+1]}

for a n=H_{o}t coordinate n_{recombination} = 6.259485×10^{-5 }or about 6.259485×10^{-5}(16.88 Gy) = 1.056601 Million years attenuated by exp{-hf/kT} = e^{-1} = 0.367879 to a characteristic cosmological time coordinate of 0.36788×1.056601 = 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=2.302736×10^{-5}) = 3.67894×10^{21} m* to R(n=6.259485×10^{-5}) = 10^{22} 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}) = 6π^{2}l_{ps}^{2}.σ.T_{nps}^{4 }= 2.6711043034×10^{96 }Watts*, where σ = Stefan’s Constant = 2π^{5}k^{4}/15h^{3}c^{2} and as a product of the defined ‘master constants’ k, h, c^{2}, π and ‘e’.

L(n,T) = 3H_{o}M_{o}.c^{2}/550n and for Temperature T(n_{ps}) ———– T(n_{ps}) = 2.93515511×10^{36 }Kelvin*.

T(n)^{4} = H_{o}M_{o}c^{2}/(2p^{2}sR_{H}^{2}[550n^{3}/[n+1]^{2}]) for T(n)^{4} = {[n+1]^{2}/n^{3}}H_{o}M_{o}c^{2}/(2p^{2}sR_{H}^{2}[550]) = 18.1995{[n+1]^{2}/n^{3}} (K^{4}/V)* for a temperature interval in using the recombination epoch coordinates T(n_{1}=6.2302736×10^{-5}) = 2945.42 K* to T(n_{2}=6.259485×10^{-5}) = 2935.11 K*

As the magnitude of the Einstein Lambda of the instanton is of the order of 2×10^{85} acceleration units and relates to the baryonic matter (BM) density in the seedling mass M_{o}/2M_{∞} =½W_{BMps}; with ‘closure’ mass M_{∞}=R_{H}.c^{2}/2G_{o}=c^{3}/2G_{o}H_{o} relates to the wormhole mass m_{ps}=hf_{ps}/c^{2} =2.222..x10^{-20} kg; as quantum eigenstate; the coupling between the Planck density r_{P}=l_{P}^{3}/m_{P}=1.85×10^{96} and the ‘critical closure’ density r_{H}=M_{∞}/R_{H}^{3} 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_{H}^{3} = hf_{ps}c^{4}/8G_{o}^{3}M_{H}^{3} = 5.45×10^{-99} .

A modular brane mirror-T duality between the inversion properties of two parts of a heterotic supermembrane (class HE(8×8)) and can be expressed in the unitary dimensions of the Gravitational Constant G_{o} in [m^{3}][kg^{-1}][s^{-2}]=(Volume)(Angular Acceleration)/(Mass)=(Angular Acceleration)/(Density).

Describing the Einstein Lambda in the form of a parametrized Curvature Radius L(n)/R_{Hubble}= L(n)H_{o}/c = L(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=mc^{2}. Brane mirror duality unifies the electromagnetic and gravitational interactions via the coupling of their finestructures. The quantization of mass m so indicates the coupling of the Planck Law in the frequency parameter to the Einstein law in the mass parameter. The postulative basis of M-Theory utilizes the coupling of two energy-momentum eigenstates in the form of the modular duality between so termed ‘vibratory’ (high energy and short wavelengths) and ‘winding’ (low energy and long wavelengths) selfstates.

The ‘vibratory’ selfstate is denoted in: E_{ps}=E_{primary sourcesink}=hf_{ps}=m_{ps}c^{2} and the ‘winding’ and coupled selfstate is denoted by: E_{ss}=E_{econdary sinksource}=hf_{ss}=m_{ss}c^{2}

The F-Space Unitary symmetry condition becomes: f_{ps}f_{ss}=r_{ps}r_{ss}=(λ_{ps}/2π)(2πλ_{ss})=1

The coupling constants between the two eigenstates are so: E_{ps}E_{ss}=h^{2} and E_{ps}/E_{ss}=f_{ps}^{2}=1/f_{ss}^{2} The Supermembrane E_{ps}E_{ss} then denotes the coupled superstrings in their ‘vibratory’ high energy and ‘winded’ low energy selfstates.

The coupling constant for the vibratory high energy describes a MAXIMISED frequency differential over time in df/dt|_{max}=f_{ps}^{2} and the coupling constant for the winded low energy describes its MINIMISED reciprocal in df/dt|_{min}=f_{ss}^{2}.

F-Theory also crystallizes the following string formulations from the E_{ps}E_{ss} superbrane parameters.

**Electromagnetic Finestructure: a _{e} = 2pke^{2}/hc = e^{2}/2e_{0}hc**

**Gravitational Finestructure (Electron): a**

_{g}= 2pG_{o}m_{e}^{2}/hc = {m_{e}/m_{Planck}}^{2}**Gravitational Finestructure (Primordial Nucleon): a**

_{n}= 2pG_{o}m_{c}^{2}/hc**Gravitational Finestructure (Planck Boson): a**

_{Planck}= 2pG_{o}m_{Planck}^{2}/hc1/E

_{ps}=e*=2R

_{e}c

^{2}=√{4αhce

^{2}/2πG

_{o}m

_{e}

^{2}}=2e√α[m

_{P}/m

_{e}=2e√{a

_{e}/a

_{g}} = {2e

^{2}/m

_{e}}√(k/G

_{o})=2e

^{2}/G

_{o}m

_{e}= e

^{2}/2pe

_{o}m

_{e}for G

_{o}= 1/k = 4pe

_{o}for the cosmological unification of the finestructures.

E

_{ps }= 1/E

_{ss}= 1/e* = √{a

_{g}/a

_{e}}/2e = G

_{o}m

_{e}/2e

^{2}

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

_{e}c

^{2}=ke

^{2}/R

_{e}; and for the electronic restmass m

_{e}. Alpha α is the electromagnetic finestructure coupling constant α=2πke

^{2}/hc for the electric charge quantum e, Planck’s constant h and lightspeed 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 protostars as a function of temperature and independent of mass. Those ‘ylem’ stars can be shown to be naturally degenerate ‘proto’ magnetars and neutron stars, whose gravitational inward pressure is balanced by their thermal heat content deriving from the Cosmic radiation temperature.

The general Jeans formulation for ylem stars is R

_{ylem}= √{kTR

_{e}

^{3}/G

_{o}m

_{c}

^{2}}, R

_{e}=e

^{2}/4pe

_{o}m

_{e}c

^{2}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 spacetime into dS spacetime.

*” Spacetime tells matter how to move; matter tells spacetime how to curve.”*

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

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

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

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

The problem of the singularity regarding the creation event, known as the Quantum Big Bang in General Relativity is well addressed in the literature of science and an appropriate solution to the infinite continuous regression of spacetime parameters is resolved in a disengagement and an unnecessity of and for a prior existing spacetime background for matter to act within.

It is the nature of the string itself, which in particular initial- and boundary conditions allows the concepts of space and time to emerge from the qualitative and quantitative nature of the string definition itself.

In particular a discretization of dynamical parameters of an describing cosmology in defined Planckian parameters serves to replace the infinite mathematical pointlike singularity to a so called Plancking string vibration formulated as the Planck length l_{Planck} and which can be considered to be a mimimum displacement as a wormhole radius.

Any displacement scale below the Planck length then is rendered unphysical and so becomes mathematically inapplicable to describe the dynamics in a physical universe, described by a cosmology, which defines a string epoch characterized by a cosmological inflationary Inflaton from a defined Planck-Length-Quantum-Oscillation/Fluctuation to a so labeled Quantum Big Bang Instanton.

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

The Inflaton defined a 11-dimensional supermembraned de Sitter closed – and positively curved cosmology with a defined Hubble Event horizon for a positive spheroidal curvature information bound.

This closed universe contained no matter seed, but was defined in its curvature through a unification condition relating the electromagnetic finestructure alpha {a=2pke^{2}/hc} to the gravitational finestructure omega {w=2pG_{o}m_{Planck}^{2}/hc} via ke^{2} = e^{2}/4pe_{o} = G_{o}M_{unification}^{2} for e^{2} = {G_{o}/k}M_{unification}^{2}

requiring dimensional mensuration identity in inflaton space [C^{2}/Jm]=[Farad/meter] = [Jm/kg^{2}] for [C] = [C*] = [StarCharge Coulomb] = [m^{3}/s^{2}] = [VolumexAngular Acceleration] and for the Maxwell Constant 1/c^{2} = m_{o}.e_{o} = {120p/c}{1/120pc} and ‘Free Space’ Inflaton Impedance Z_{o}= electric field strength E/magnetic field strength H = √(m_{o}/e_{o}) = cm_{o} = 1/ce_{o} = 120p}.

Therefore,

[G_{o}]_{mod} =[4pe_{o}]_{mod} = [1/k]_{mod} and the inflaton dimensionless string modular unity is G_{o}k=1 for e^{2} = G_{o}^{2}.M_{unification}^{2} = M_{unification}^{2}/k^{2} 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 supersymmetry of the Planck superstring class I at the Planck energy level to the monopole superstring energy of superstring class IIB with the Planck mass being replaced by 30 monopole masses as the integration of 30 [ec] monopole masses at the [ec^{3}]_{mod} = 2.7×10^{16} GeV energy level of the Grand Unification Energy separating the quantum gravity from the GUT symbolized as SEW.G.

Setting w=1 defines the Planck-Mass and setting a proto-nucleon seed m_{c}=m_{Planck}.a^{9} allows the breaking of the inflaton supersymmetry in the superstring classes.

Replacing the protonucleon mass m_{c }= √{hc/2pG_{o}}.{60pe^{2}/h}^{9} = 9.924724523x 10^{-28} kg by the effective electron mass m_{e} = ke^{2}/2G_{o}(1.125×10^{12}) =9.290527148×10^{-31 }kg sets the Electromagnetic Interaction/Gravitational Interaction ratio **EMI/GI = e ^{2}/G_{o}^{2}m_{e}^{2} = {e/G_{o}m_{e}}^{2} = 2.421821677×10^{42 }**using string units.

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

**Modular String Duality and the Wormhole Curvature Boundary **

The concept of modular (Mirror/T) duality in supermembrane theory relates a maximum or large spacial displacement radius R as a low frequency and low energy named as a ‘winding mode’ to its inverse minimum or small spacial displacement radius 1/R as a high frequency and high energy as a ‘vibratory mode’.

The utility of either ‘string mode’ would then result in an identical physical description either using a ‘macroquantum’ radius R or a ‘microquantum’ radius 1/R.

c = l_{min}.f_{max} = 2pR_{min}.f_{max} as lightspeed invariance for the vibratory string mode R_{curvature} = R_{min} = l_{min} /2p = Wormhole Perimeter/2p

1/c = 1/(l_{min}.f_{max}) = l_{max}.f_{min} = l_{max}/f_{max} = R_{max}.f_{min}/2p as lightspeed invariance for the winding string mode R_{curvature} = R_{max} = 2p.l_{max} = 2p/Wormhole Perimeter

For the Harmonic Planck Energy Oscillator Energy E^{o} = ½hf_{o} = ½m_{o}c^{2} = ½kT_{Planck}

Planck Mass = m_{Planck} = √{hc/2pG_{o}}

Planck Energy = E_{Planck} = m_{Planck}.c^{2} = √{hc^{5}/2pG_{o}} = hf_{Planck} = hc/l_{Planck} = kT_{Planck}

Planck Length = l_{Planck} = l_{Planck}/2p = √{hG_{o}/2pc^{3}}

Planck Temperature = T_{Planck} = E_{Planck}/k = √{hc^{5}/2pk^{2}G_{o}}

Planck Density = ρ_{Planck}= m_{Planck}/V_{Planck} = √{4p^{2}c^{10}/h^{2}G_{o}^{4}}/2p^{2} = c^{5}/phG_{o}^{2}= 9.40×10^{94} kg/m^{3} for 9×10^{60} permutation vibratory string eigenstates by |f_{ps}^{2}|_{mod}.

Energy Density Inflaton/Energy Density Instanton = E_{Planck}.V_{BigBang}/E_{BigBang}V_{Planck }with minimum Inflaton Planck Oscillator: E^{o}_{Planck} = ½m_{Planck}c^{2}

= m_{Planck}.r_{wormhole}^{3}/m_{wormhole}.l_{Planck}^{3} = √{(hc/2pG_{o})(2pc^{3}/hG_{o})}(2pc^{3}/hG_{o})(r_{wormhole}^{3}/m_{wormhole}} = (c^{2}/G_{o})(2pc^{3}/hG_{o}){r_{wormhole}^{3}/m_{wormhole}}

= (2pc^{5}/hG_{o}^{2}){r_{wormhole}^{3}/m_{wormhole}} = {4p^{2}k^{2}/h^{2}G_{o}} (hc^{5}/2pG_{o}k^{2}){r_{wormhole}^{3}/m_{wormhole}} = {kT_{Planck}}^{2}(2pr_{wormhole})^{2}{1/h^{2}G_{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}}{c^{2}/G_{o}m_{wormhole}} for the minimum Instanton Planck Oscillator: E^{o}_{Planck} = ½m_{wormhole}c^{2}

V_{BigBang}/V_{Planck }= {E_{Planck}/E_{BigBang}}.{r_{wormhole}}{c^{2}/G_{o}m_{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..x10^{23} in string units.

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

It has been discovered, that the universe contains an intrinsic coupling-parameter between its inertial masscontent and its noninertial energy content.

The matter in the universe is described by the physical parameter termed Mass (M), say as proportional to Energy (E) in Einstein’s famous equation Mass M=E/c^{2}.

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 kinetematic velocity as the ratio of displacement over time generalised in the lightpath 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=mc^{2} (The Combined Planck-Einstein Law)

(2) E=hf iff m=0 (The Planckian Quantum Law E=hf for lightspeed invariance c=λf)

(3) E=mc^{2} iff f=f_{o}=f_{ss} (The Einstein Law E=mc^{2} for the lightspeed 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: E^{2}=E_{o}^{2}+(pc)^{2}} by the photonic momentum p=h/λ=hf/c} OR a ‘restmass’ m_{o}=m/√[1-(v/c)^{2}] for ‘restenergy’ E_{o}=m_{o}c^{2}.

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

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

(3) If M>0, then there exists a mass-eigen frequency f_{ss}=f_{o}=E_{ss}/h=m_{ss}c^{2}/h, which QUANTIZES all mass agglomerations m=Σm_{ss} in the massquantum m_{ss}=E_{ss}/c^{2}.

**The Wave Matter of de Broglie: l _{deBroglie} = h/p **

__https://youtu.be/-IfmgyXs7z8__ __https://youtu.be/tQSbms5MDvY__

The Wavematter of de Broglie from the Energy-Momentum Relation is applied in a (a) nonrelativistic, a (b) relativistic and a (c) superluminal form

in the matter wavelength: **l _{deBroglie} = h/p = hc/pc for (pc) = √{E^{2} – E_{o}^{2}}= m_{o}c^{2}.√{[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 = 6.7×10^{-33} m

This matter wavelength requires diffraction interference pattern of the order of l_{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_{o}c^{2} with E = mc^{2} = m_{o}c^{2}/√{1-[v/c]^{2}}, a 66.66% increase in the electron’s energy describing the Kinetic Energy E – E_{o} = {m – m_{o}}c^{2} for a relativistic momentum p = m_{o}c.√{[0.8]^{2}/(1-[0.8]^{2})} = (1.333..) m_{o}c = h/l_{deBroglie} and for a relativistic de Broglie wavelength, 60% smaller, than for the nonrelativistic electron in l_{deBroglie }= h/1.333..m_{o}c < h/0.8m_{o}c = l_{deBroglie} (1.83×10^{-12} m relativistic and 3.05×10^{-12} m nonrelativistic for an electron ‘restmass’ of 9.11×10^{-31} kg and measurable in diffraction interference patterns with apertures comparable to this wavematter scale)

(c) The de Broglie matter wavespeed in its ‘group integrated’ form derives from the postulates of Special Relativity and is defined in the invariance of light speed ‘c’ as a classical upper boundary for the acceleration of any mass M.

In its ‘phase-individuated’ form, the de Broglie matter wave is ‘hyperaccelerated’ or tachyonic, the de Broglie wave speed being lower bounded by light speed ‘c’

**v _{phase} = wavelength.frequency = (h/mv_{group})(mc^{2}/h) = c^{2}/v_{group} > c for all v_{group} < c**

m = Energy/c^{2} = hf/c^{2} = hc/l_{deBroglie}c^{2} = h/l_{deBroglie}c = m_{deBroglie} = [Action as Charge^{2}]_{mod}/c(Planck-Length Oscillation)

= [2pe^{2}]_{mod}/cl_{dPlanck}√alpha = [e^{2}c^{2}/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*/c^{2} = [ec]_{modular}** as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy quantum

**E**

_{ps}=hf_{ps}=m_{ps}c^{2}=kT_{ps}as a function of

**e*=1/E**of Heterotic superstring class HE 8×8

_{ps}and relating the

**Classical Electron Diameter {2R**

_{e}} as Monopole Mass [ec]_{mod}in Curvature Radius r_{ps}=l_{ps}/2p = G_{o}m_{ps}/c^{2}**The factor 2G _{o}/c^{2} multiplied by the factor 4p becomes Einstein’s Constant k = 8pG_{o}/c^{2} = 3.102776531×10^{-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_{e}c^{2}/30[ec^{3}]_{mod} = e*/30[ec^{3}]_{mod} ∝ k for a proportionality constant**

{k*}=2R_{e}/30k[ec]_{mod} = 2R_{e}.c^{2}/8pe = e*/8pe =1.2384..x10^{20} kg/m in string units for StarCharge in Star Colomb C*/ElectroCharge in Coulomb C unified.

The monopolar Grand Unification (SEWG gravitational decoupling SEW.G) has a Planck string energy reduced at the IIB string level of

**e*=[ec ^{3}]_{modular} **for

**m**= 2.7×10

_{ps}c^{2}c/[ec]_{modular}= [c^{3}]_{modular}^{25}electron volt or 4.3362×10

^{6}J for a monopole mass [ec]

_{modular }= m

_{monopole }= 4.818×10

^{-11}kg .

**Mass M = n.m _{ss} = Sm_{ss} = n.{h/2pr_{deBroglie}c} .[E_{ss}.e*]_{mod} = n.m_{ps}.[E_{ss}.{9×10^{60}}.2p^{2}R_{rmp}^{3}]_{mod} = n.m_{ps}.[E_{ss}.{2R_{e}.c^{2}}]_{mod} = n.[E_{ps}.E_{ss}]_{mod}.[2R_{e}]_{mod}**

for l_{deBroglie}=l_{ps}=h/m_{ps}c and [E_{ps}.e*]_{mod} =1

{2R_{e}c^{2}} = 4G_{o}M_{Hyper} for the classical electron radius R_{e}=ke^{2}/m_{e}c^{2} and describes its HyperMass M_{Hyper-electron} = R_{e}c^{2}/2G_{o} = ke^{2}/2G_{o}m_{e} = 1.125×10^{12} kg for an effective electron mass of m_{e} = ke^{2}/2G_{o}(1.125×10^{12}) =9.290527148×10^{-31 }kg in string units and where k=1/4pe_{o }= 9×10^{9} Nm^{2}/C^{2}.

The curvature radius for the electron mass m_{e} = r_{electron}c^{2}/2G_{o} then becomes **r _{electron} = 2G_{o}m_{e}/c^{2} = 2.293957…x10^{-57} m in string-membrane inflaton space as 1.44133588×10^{-34}r_{ps} in the wormhole instanton space. **

**R _{e}/r_{inflaton-electron} = M_{Hyper-electron}/m_{e} = 1.2109108..x10^{42} = ½(EMI/GI) = ½(e^{2}/G_{o}^{2}m_{e}^{2}) =½ {e/G_{o}m_{e}}^{2} = ½(2.421821677×10^{42 }**) 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

_{ps}E

_{ss}=h

^{2 }and E

_{ps}/E

_{ss}=f

_{ps}

^{2}=1/f

_{ss}

^{2}.

**Mass M = n.m _{ss} = Sm_{ss} = n.{m_{ps}} .[E_{ss}.e*]_{mod} = n.{m_{ps}}[{hf_{ss}}{f_{ps}/f_{ss}}.2p^{2}R_{rmp}^{3}]_{mod} = n.m_{ps}.[E_{ps}.e*/f_{ss}^{2}]_{mod} = n.m_{ps}/|f_{ss}^{2}|_{mod}**

**HyperMass and the Hawking Modulus in Curvature of Spacetime**

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_{o}M/c^{2}**

for HyperMass:—————-M_{Hyper} = hc^{3}.e*/4pG_{o} = ½N_{Avagadro-Instanton}.m_{wormhole}

HyperMass 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)/c^{2} = 1.728..x10^{-25} meters.

This is below the boundary condition of r_{min} = 10^{-22}/2p m = 1.591549..x10^{-23} m for which the minimum mass requirement is found to be 6445.775.. kg.

This result shows, that no physical microquantum Black Holes can exist, but that the minimum unitary wormhole quantum of the Instanton is given by a ‘wormhole substance’ or Inflaton Black Hole Molarity count for a new minimum Planck Oscillator at the HE 8×8 Instanton energy scale **E ^{o}_{BigBang}=½m_{ps}c^{2}=½hf_{ps}=½kT_{ps}=½E_{ps}=1/2e***

**M _{Hyper}/½m_{ps} = 2hc^{3}.e*/4pG_{o}.m_{ps} = N_{Avagadro-Instanton }= r_{ps}/R_{ps}**for hypermass

N_{Avagadro-Instanton} = 5.8012×10^{23 }

**M**

_{Hyper}= hc^{3}.e*/4pG_{o}= ½N_{Avagadro-Instanton}.m_{wormhole}for

**R**

_{ps }= G_{o}m_{ps}/c^{2}= r_{ps}/N_{Avagadro-Instanton }= 2.743…x10^{-47}m in Inflaton membrane space of 11D and string space of 10DM_{Hyper}/m_{min} = M_{min}/m_{min} = {n.hc^{3}e*/4pG_{o}}/m_{min} = {n.r_{min}c^{2}/2G_{o}}/m_{min} = {hc^{3}.c^{2}/4pG_{o}E_{min}}{ne*} = {hc^{3}.c^{2}/4pG_{o}hf_{min}}{ne*} = {2pr_{min}.hc^{3}.c^{2}/4pG_{o}hc}{ne*} = {r_{min}.c^{2}.E/2G_{o}M}{ne*} = r_{min}/R.{Ene*} for R = 2G_{o}M/c^{2 }

for a generalized energy-mass proportionality c^{2}=E/M in modular membrane duality with ne* = 1/E and ne*E = 1 (Modular Unification) for ** n.e*hc = n.l _{min}.**

m_{Hyper}/r_{min} = {r_{min}c^{2}/2G_{o}}/r_{min} = c^{2}/2G_{o} = n.m_{min}.Ee*/R = M/R_{curv} for de Broglie wave matter m_{min} = hf_{min}/c^{2} = h/cl_{min}

Utility of the Schwarzschild metric allows calculation of Black Hole matter equivalents for any mass **M>r _{min}c^{2}/2G_{o} **say for a planetary mass M

_{Earth}= 6×10

^{24}kg for a r

_{curv}= 0.015 meters and for a solar mass M

_{Sun}= 2×10

^{30}kg for a r

_{curv}= 4938.3 meters.

The curvature of the Inflaton calculates as R_{Hubble-11D} = c/H_{o} = 2G_{o}M_{BigBang-Seed}/c^{2} = 1.59..x10^{26} meters for the Inflaton Mass of 6.47..x10^{52} kg.

For any mass **M<r _{min}c^{2}/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 m = GM = constant = G_{o}M(X^{n}Y^{n})= G_{o}X^{n}.MY^{n} and for (XY)^{n}=1 can be finestructured in a decreasing gravitational constant G(n)=G_{o}X^{n} with a corresponding increase in the mass parameter M as M(n)=M_{o}Y^{n} as say for the proto-nucleonic mass of the Instanton m_{c}(n_{ps}) as m_{c}(n_{present}) = m_{c}.Y^{npresent} = m_{neutron }< m_{c}Y^{npresent} = 1.711512476..x10^{-27} kg upper limited

For a changing Gravitational constant G(n_{present}) .m_{neutron}(n_{present})^{2} = G_{o}m_{c}^{2}.Y^{npresent} and is modulated say in A micro-macro Black Hole perturbation M_{o}^{2}/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/2pG_{o}}{½m_{Planck}.c^{2}/k} = hc^{3}/4pG_{o}k = {M_{Smin}**.

**T**

= 9.131793821×10

_{Smax}} = {m_{ps}.T_{ps}.½N_{Avagadro-Instanton}} = [c^{2}/4p^{2}]_{mod}.{M_{MaxHawking}.T_{Smin}}= 9.131793821×10

^{23}kgK with (m_{ps}T_{ps}= E_{ps}^{2}/kc^{2 }= 1.002117..p)The Hawking Modulus so has mensuration units [Mass][Temperature] in [kg][K(elvin)], which reduce to [Mass]{Energy] in [kg][J(oules)] for ignoring the Stefan-Boltzmann entropy constant k.

And so M_{min}.T_{max }= hc³/4πG_{o}k = [c^{2}/4π^{2}]_{mod}.M_{max}.T_{min }= ½m_{Planck}.T_{Planck }= M_{MaxHawking}. [c^{2}/4π^{2}]_{mod}.T_{ss} and the Hawking Mass is determined as M_{MaxHawking} = λ_{max}πc²/G_{o} = 2.54469..x10^{49} kg*.

HyperMass **M _{Hyper} (n_{ps}) = hc^{3}.e*/4pG_{o} = ½N_{Avagadro-Instanton}.m_{wormhole}** = 6445.775 kg at the Instanton boundary n=n

_{ps}so increases to

**M**~ 11,115.59 kg as the projected Instanton boundary mass for the wormhole radius

_{Hyper}(n_{present})Y^{npresent}=hc^{3}.e*/4pG_{o}X^{npresent }**r**modulating the Inflaton curvature with the Instanton curvature and utilizing n

_{wormhole}= r_{ps}= N_{Avagadro-Instanton}.R_{ps}_{present}=1.1324.. for a decreased perturbed G(n

_{present}) = 6.443×10

^{-11}G-string units for the Standard Gravitational Parameter G(n)m

_{i}Y

^{k}(n).m

_{j}Y

^{n-k}= G

_{o}m

_{c}

^{2}= constant for G(n)=G

_{o}X

^{n}.[/b]

For a present measured neutron mass of 1.674927×10^{-27 }kg = 939.5656 MeV in the [SI} system of measurement, the string values are (1.674927×10^{-27})(1.003753127) = 1.681212..x10^{-27} kg* or (939.5656)(1.005102826){e-/e-*} = (939.5656)(1.005102764)/(1.002671189) = 941.844 MeV*

Using the λ_{min}λ_{max}=1 wavelength modulation in the T/Mirror 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_{o}^{2}/2M_{∞}.M_{Max}=M_{o}^{2}/8π.M_{∞}.M_{Hawking}=3.2895..x10^{102}/3.2931..x10^{102} ~ 0.9989…

(More details are described in 7. Newton’s Gravitational Constant Measurements following. this excerpt.)

“This also circumscribes the actual to critical density ratio in the omega of the general relativistic treatment of the cosmologies.

Now recall our applied G value in G_{m}(n)=G_{o}.and apply our just derived Black Hole Mass modulation coupled to that of the quantum micromasses.

We had: G_{o}m_{c}²={G_{o}X^{n+k}}.{m_{c}Y^{n}}.{m_{c}Y^{k}}=G_{m}.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_{o}m _{c}²/m_{nmax}.m_{nmin}=G_{o}m_{c}²/({m_{c}Y^{n}}{m_{nmin}}) and where we have m_{nmin}=m_{c}Y^{k}} for the unknown value of k.

So G_{m}(n)=G_{o}.X^{n+k}=G_{o}X^{n}[m_{c}/m_{nmin}]=G_{o}{m_{c}^{2}/m_{c}Y^{n}}.{M_{o}^{2}/8π.M_{∞}.M_{Hawking}.m_{av}}} and where now {m_{nmin}}={m_{c}Y^{k}}={8π.M_{∞}.M_{Hawking}.m_{av}/M_{o}^{2}}=1.0011..m_{av}.

m_{av}={M_{o}²/8π.M_{∞}.M_{Hawking}}{m_{nmin}}={M_{o}²/8π.M_{∞}.M_{Hawking}}{m_{c}Y^{k}}=0.9989..{m_{c}Y^{k}} and obviously represents a REDUCED minimum mass m_{nmin}=m_{c}Y^{k}.

But the product of maximum and ‘new’ minimum now allows an actual finetuning to a MEASURED nucleon mass m_{N} by: m_{N}² = m_{av}Y^{n}.m_{c}Y^{n}=m_{av}.m_{nmax}.Y^{n}.

So substituting for m_{av} in our G_{m} expression, will now give the formulation:

G_{m}(n)=G_{o}.X^{n+k}=G_{o}X^{n}[m_{c}/m_{nmin}]=G_{o}{m_{c}^{2}/m_{c}Y^{n}}.{M_{o}^{2}/8π.M_{∞}.M_{Hawking}.m_{av}}

G_{m}(n)=G_{o}.X^{n+k}=G_{o}X^{n}[m_{c}/m_{nmin}]=G_{o}{m_{c}^{2}/m_{c}Y^{n}}.{M_{o}^{2}/8π.M_{∞}.M_{Hawking}}{m_{c}Y^{2n}/m_{N}^{2}} and where {M_{o}^{2}/8π.M_{∞}_{.}M_{Hawking }= 0.9989..}

G_{m}(n)=G_{o}.{m_{c}^{2}/m_{N}^{2}}{M_{o}^{2}/8π.M_{∞}.M_{Hawking}}Y^{n}

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.

For a Neutron Restmass of: m_{n}=1.680717×10^{-27} kg* (941.6036 MeV*) the substitution (and using calibrations

m=1.001671358 m*; s=1.000978395 s*; kg=1.003753127 kg* and C=1.002711702 C* gives G(n_{p})=6.678764×10^{-11} (m^{3}/kgs^{2}) and a perturbation corrected m_{n}=1.681100563×10^{-27} kg* (941.818626 MeV*) gives: m_{neutron} = 1.67481477×10^{-27} kg

G(n_{p}) = G_{o}{m_{c}/m_{N}}^{2}.(0.9989..) = 6.67093×10^{-11} (m^{3}/kgs^{2})* or 6.675547×10^{-11} (m³/kgs²).

The perturbation upper limit is given in the m_{n}=1.681335×10^{-27} kg* (941.9506 MeV*) and gives:

G(n_{p}) = G_{o}{m_{c}/m_{N}}^{2}.(0.9989..) = 6.6690685×10^{-11} (m^{3}/kgs^{2})* or 6.673685×10^{-11} (m³/kgs²).

**The average for the last two values then approximates as a ‘best fit’ for: G _{m}(n_{p}) = ½{6.67093×10^{-11} + 6.6690685×10^{-11}} (m^{3}/kgs^{2})* = 6.6699925×10^{-11} (m^{3}/kgs^{2})* or G_{m}(n_{p}) = ½{6.675547×10^{-11} + 6.673685×10^{-11}} (m^{3}/kgs^{2}) = 6.674816×10^{-11} (m^{3}/kgs^{2}) **

This is a best-fit approximation, considering the uncharged nature of the testmasses.

This then gives the value of k from G_{m}(n)=G_{o}.X^{n+k} as k=ln(G_{m}Y^{n}/G_{o})/lnX and which calculates as k= -0.073387..”