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

As the magnitude of the Einstein Lambda of the instanton is of the order of 2x1085 acceleration units and relates to the baryonic matter (BM) density in the seedling mass Mo/2M =½ΩBMps; with 'closure' mass M=RH.c2/2Go=c3/2GoHo relates to the

wormhole mass mps=hfps/c2 =2.222..x10-20 kg; as quantum eigenstate; the coupling between the Planck density ρP=lP3/mP=1.85x1096 and the 'critical closure' density ρH=M/RH3 becomes subject to the overall mass evolution from the wormhole mass to the

'closure mass' over the evolution cycle, ending after for nreset=234.5 for 3.96 Trillion years.

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

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


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

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

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

The coupling constants between the two eigenstates are so: EpsEss=h2 and Eps/Ess=fps2=1/fss2

The Super-membrane EpsEss then denotes the coupled superstrings in their 'vibratory' high energy and 'winded' low energy self states.

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

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


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

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

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

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


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


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

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

Re is the 'classical electron radius' coupling the 'point electron' of Quantum- Electro-Dynamics (QED) to Quantum Field Theory (QFT) and given in the electric potential energy of Coulomb's Law in: mec2=ke2/Re; and for the electronic restmass me.

Alpha α is the electromagnetic fine structure coupling constant α=2πke2/hc for the electric charge quantum e, Planck's constant h and light speed constant c.

Go is the Newtonian gravitational constant as applicable in the Planck-Mass mP=√(hc/2πGo).

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

The universe begins with a baryon matter seed of 2.813% in AdS spacetime, which allows the emergence of a first generation family of 'eternal' Black Holes to seed 'eternal' White Holes manifesting as quasars which seed galaxies from a first generation of 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 Rylem = √{kTRe3/Gomc2}, Re=e2/4πεomec2 and mc is a prototypical nucleon mass.

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

wheeler-.37155.



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 lPlanck 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 = 2πGomPlanck2/hc}

via ke2 = e2/4πεo = GoMunification2 for e2 = {Go/k}Munification2   requiring dimensional mensuration identity in inflaton space [C2/Jm]=[Farad/meter] = [Jm/kg2] for [C] = [C*] = [Star-Charge Coulomb] = [m3/s2] = [VolumexAngular Acceleration] and for the Maxwell

Constant 1/c2 = μoo = {120π/c}{1/120πc} and 'Free Space' Inflaton Impedance Zo= electric field strength E/magnetic field strength H = √(μoo) = cμo = 1/cεo = 120π}.

Therefore,
[Go]mod =[4πεo]mod = [1/k]mod and the inflaton dimensionless string modular unity is Gok=1 for e2 = Go2.Munification2 = Munification2/k2 and Munification = 30[ec] that is 30 modulated magnetic monopole masses. It is this 30[ec]modular inflaton mass, which

represents the initial breaking of the inherent 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 mc=mPlanck9 allows the breaking of the inflaton super-symmetry in the superstring classes.

Replacing the proto-nucleon mass mc = √{hc/2πGo}.{60πe2/h}9 = 9.924724523x 10-28 kg by the effective electron mass me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg sets the Electromagnetic Interaction/Gravitational Interaction ratio

EMI/GI = e2/Go2me2 = {e/Gome}2 = 2.421821677x1042 using string units.


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

hayes-.37157.




Modular String Duality and the Wormhole Curvature Boundary

The concept of modular (Mirror/T) duality in 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.fmax = 2πRmin.fmax as light speed invariance for the vibratory string mode Rcurvature = Rmin = λmin /2π = Wormhole Perimeter/2π

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

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

Planck Mass = mPlanck = √{hc/2πGo}

Planck Energy = EPlanck = mPlanck.c2 = √{hc5/2πGo} = hfPlanck = hc/lPlanck = kTPlanck

Planck Length =lPlanck = λPlanck/2π = √{hGo/2πc3}

Planck Temperature = TPlanck = EPlanck/k = √{hc5/2πk2Go}

Planck Density = ρPlanck= mPlanck/VPlanck = √{4π2c10/h2Go4}/2π2 = c5/πhGo2= 9.40x1094 kg/m3 for 9x1060 permutation vibratory string eigenstates by |fps2|mod.

Energy Density Inflaton/Energy Density Instanton = EPlanck.VBigBang/EBigBangVPlanck with minimum Inflaton Planck Oscillator: EoPlanck = ½mPlanckc2

= mPlanck.rwormhole3/mwormhole.lPlanck3 = √{(hc/2πGo)(2πc3/hGo)}(2πc3/hGo)(rwormhole3/mwormhole} = (c2/Go)(2πc3/hGo){rwormhole3/mwormhole}

= (2πc5/hGo2){rwormhole3/mwormhole} = {4π2k2/h2Go} (hc5/2πGok2){rwormhole3/mwormhole} = {kTPlanck}2(2πrwormhole)2{1/h2Go}{rwormhole/mwormhole}

= {EPlanck}2.{c/hfwormhole}2.{1/Go}}{rwormhole/mwormhole} = {EPlanck/EBigBang}2.{rwormhole}{c2/Gomwormhole} for the minimum Instanton Planck Oscillator: EoPlanck = ½mwormholec2
VBigBang/VPlanck = {EPlanck/EBigBang}.{rwormhole}{c2/Gomwormhole} for EVBigBang/EVPlanck = EVInstanton/EVInflaton = rwormhole/Rowormhole = NAvagadro-Instanton and counting the amount of wormhole string transformed from the Inflaton as the Instanton of the Quantum

Big Bang and as the constant 5.801197676..x1023 in string units.





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

It has been discovered, that the universe contains an intrinsic coupling-parameter between its inertial 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 (Mi) as being proportional to some applied Force (F) or the 'work done' for a particular displacement {F=dp/dt for p=mv and v a 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 Mi has a gravitational counterpart described not by the change in momentum of inertia carrying matter agglomerations; but by the geometric curvature of space containing matter conglomerations. This Gravitational Mass Mg is measured to be equivalent to the Inertial Mass Mi and is formulated in the 'Principle of Equivalence' in Einstein's Theory of General Relativity.
F-Theory then has shown, that this Inertial Mass Mi is coupled inherently to a 'mass-eigen' frequency via the following formulation:

(1) Energy E=hf=mc2 (The Combined Planck-Einstein Law)

(2) E=hf iff m=0 (The Planck Quantum Law E=hf for light speed invariance c=λf)

(3) E=mc2 iff f=fo=fss (The Einstein Law E=mc2 for the light speed upper limit)

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

The 'total' energy for the occupied space so contains a 'variable' mass in the 'combined' law; but allows particularisation for electromagnetic radiation (always moving at the Maxwell 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 fss=fo=Ess/h=mssc2/h, which QUANTIZES all mass agglomerations m=Σmss in the mass quantum mss=Ess/c2.


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


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: λdeBroglie = h/p = hc/pc for (pc) = √{E2 - Eo2}= moc2.√{[v/c]2/(1-[v/c]2)}

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


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

Eo = moc2 with E = mc2 = moc2/√{1-[v/c]2}, a 66.66% increase in the electron's energy describing the Kinetic Energy E - Eo = {m - mo}c2  for a relativistic momentum p = moc.√{[0.8]2/(1-[0.8]2)} = (1.333..) moc = h/λdeBroglie and for a relativistic de Broglie

wavelength, 60% smaller, than for the non-relativistic electron in  λdeBroglie = h/1.333..moc < h/0.8moc =λdeBroglie (1.83x10-12 m relativistic and 3.05x10-12 m* non-relativistic for an electron 'restmass' of 9.11x10-31 kg* and measurable in diffraction interference

patterns with apertures comparable to this wavematter scale).


(c) The de Broglie matter 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'

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

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

as monopole mass of GUT-string IIB and as string displacement current mass equivalent for the classical electron displacement 2Re = e*/c2 = [ec]modular as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy

quantum Eps=hfps=mpsc2=kTps as a function of e*=1/Eps of Heterotic superstring class HE 8x8 and relating the Classical Electron Diameter {2Re} as Monopole Mass [ec]mod in Curvature Radius rpsps/2π = Gomps/c2.

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

The selfduality of the superstring IIB aka the Magnetic Monopole selfstate in GUT Unification 2Re/30[ec]mod = 2Rec2/30[ec3]mod = e*/30[ec3]modκ for a proportionality constant {κ*}=2Re/30k[ec]mod = 2Re.c2/8πe = e*/8πe =1.2384..x1020 kg*/m* in string units for 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 mpsc2c/[ec]modular = [c3]modular = 2.7x1025 electron volt or 4.3362x106 J for a monopole mass

[ec]modular = mmonopole = 4.818x10-11 kg* .

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

{2Rec2} = 4GoMHyper for the classical electron radius Re=ke2/mec2 and describes its Hyper-Mass MHyper-electron = Rec2/2Go = ke2/2Gome = 1.125x1012 kg* for an effective electron mass of me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg* in string units

and where k=1/4πεo = 9x109 (Nm2/C2)*.

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

Re/rinflaton-electron = MHyper-electron/me = 1.2109108..x1042 = ½(EMI/GI) = ½(e2/Go2me2) =½ {e/Gome}2 = ½(2.421821677x1042 ) for the classical electron radius Re halved from the classical electron diameter 2Re from the definition for the modulated

supermembrane coupled in EpsEss=h2 and Eps/Ess=fps2=1/fss2.

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


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

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

Curvature Radius: ------------RCurvature = 2GoM/c2

for Hyper-Mass:----------------MHyper = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole

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

Using the Schwarzschild metric for a mass of 70 kg would calculate a Curvature Radius for a mass equivalent Black Hole of (2.22..x10-10)(70)/c2 = 1.728..x10-25 meters*.

This is below the boundary condition of rmin = 10-22/2π m = 1.591549..x10-23 m* for which the minimum mass requirement is found to be 6445.775.. kg*.

This result shows, that no physical microquantum Black Holes can exist, but that the minimum unitary wormhole quantum of the Instanton is given by a 'wormhole substance' or Inflaton Black Hole Molarity count for a new minimum Planck Oscillator at the HE

8x8 Instanton energy scale EoBigBang=½mpsc2=½hfps=½kTps=½Eps=1/2e*

MHyper/½mps = 2hc3.e*/4πGo.mps = NAvagadro-Instanton = rps/Rps

NAvagadro-Instanton = 5.8012x1023 for hypermass

MHyper = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole

for Rps = Gomps/c2 = rps/NAvagadro-Instanton = 2.743...x10-47 m* in Inflaton membrane space of 11D and string space of 10D

MHyper/mmin = Mmin/mmin = {n.hc3e*/4πGo}/mmin = {n.rminc2/2Go}/mmin = {hc3.c2/4πGoEmin}{ne*} = {hc3.c2/4πGohfmin}{ne*} = {2πrmin.hc3.c2/4πGohc}{ne*} = {rmin.c2.E/2GoM}{ne*} = rmin/R.{Ene*} for R = 2GoM/c2

for a generalized energy-mass proportionality c2=E/M in modular membrane duality with ne* = 1/E and ne*E = 1 (Modular Unification) for n.e*hc = n.λmin.

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

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

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

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

tmin=tps=1/fps=[fss]mod

The Standard Gravitational Parameter μ= GM = constant = GoM(XnYn)= GoXn.MYn and for (XY)n=1 can be finestructured in a decreasing gravitational constant G(n)=GoXn with a corresponding increase in the mass parameter M as M(n)=MoYn as say for the

proto-nucleonic mass of the Instanton mc(nps) as mc(npresent) = mc.Ynpresent = mneutron < mcYnpresent = 1.711752..x10-27 kg* and 958.99 MeV* upper limited

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

 

friedmann6. ufoqrpdf.


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

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

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

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

Hyper-Mass MHyper (nps) = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole = 6445.775 kg at the Instanton boundary n=nps so increases to MHyper(npresent)Ynpresent =hc3.e*/4πGoXnpresent ~ 11,117.26 kg as the projected Instanton boundary mass for the wormhole

radius rwormhole = rps = NAvagadro-Instanton.Rps modulating the Inflaton curvature with the Instanton curvature and utilizing npresent=1.1327... for a decreased perturbed G(npresent) = 6.442x10-11 G-string units for the Standard Gravitational Parameter

G(n)miYk(n).mjYn-k = Gomc2 = constant for G(n)=GoXn.

 

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

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

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

Gm(n)=Go.Xn+k=Gomc²/mnmax.mnmin=Gomc²/({mcYn}{mnmin}) and where we have mnmin=mcYk} for the unknown value of k with mnmax=mcYn.

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

mav={Mo²/8π.M.MHawking}{mnmin}={Mo²/8π.M.MHawking}{mcYk}=0.9989107..{mcYk} and obviously represents a REDUCED minimum mass mnmin=mcYk.

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

So substituting for mav in our Gm expression, will now give the formulation:

Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking.mav}
 
Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking}{mcY2n/mN2}
 
Gm(n)=Go.{mc2/mN2}{Mo2/8π.M.MHawking}Yn

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

baryogenesis.

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

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

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

The upper value of the neutron bound so represents an upper limit for the Gravitational Constant as the original quark-lepton bifurcation of the X-Boson precursor given in the KKK kernel. Only the KKK kernel is subject to the mass evolution of the cosmos; the leptonic masses being intrinsically incorporated in the Kernel means.

The mc.Yn so serves as an appropriate upper bounded approximation for G(n), subject to leptonic ring IR-OR perturbations.​

 

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

(Here Omega is a gauge string factor coupling in the fundamental force interactions as: Cuberoot(Alpha):Alpha:Cuberoot(Omega):Omega and for Omega=G-alpha.)

KKK-Kernelmass=Up/Down-HiggsLevel=3x319.66 MeV*= 958.99 MeV*, using the Kernel-Ring and Family-Coupling Constants.

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

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

Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).

Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

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

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

Generally using the exponential series expansion, one can indicate the change in G.

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

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

 

At timeinstantenuity of the Quantum Big Bang, n=npsps/Rmax=6.2591x10-49 ~ 0

Then GBigBang=GoXnps=Go (to 50 decimal places distinguishing the timeinstanton from the Nulltime as the Planck-Time transform).
Go represents the quantum gravitational constant applicable for any Black Hole cosmology and can be used to correlate the MOND gravitation with the Newton-Einstein gravitation (previously stated in section 3.8).

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

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

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

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