The Accelerating Universe, Dark Energy And The Alpha Variation

The Accelerating Universe, Dark Energy and the Alpha Variation​

Abstract
The experimental data collected by the various supernova observers, and under utility of the Hubble Space Telescope to track the brightness variations of discovered supernovae type Ia to the conclusion, that distant supernovae are between 20% and 30% dimmer than expected and as a consequence of their measured redshift they appear to be further away than theory permits.

An interpretation of this discovery implies, that the universe's expansion is accelerating; the measured redshift depicting a distance further away for a dimmer brightness than anticipated by theory.
Why is there a redshift gap between z=0.11 and z=0.30 approximately?
Does this imply a scarcity of supernovas in this redshift interval or is there a cosmological reason for this gap? Is this cosmological reason at the core of the Dark Energy implication and the 'factuality' of an accelerating universe?

This paper shall elucidate the cosmological nature of Dark Energy and the inferred accelerating cosmology of an accelerating universe, stipulated to begin some 5-6 Billion years ago and as a change from a measured deceleration from light speed in the early universe.

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A white dwarf star is important as a distance indicator for the cosmic distances. Should it be in a binary system with another star in mutual orbit about each other, then mass can transfer via magnetic activity from the companion star and the Chandrasekhar limit referring to gravitational collapse of about 1.5 solar masses or 3x1030 kg might so become exceeded and the white dwarf explodes as a supernova type Ia.

Supernovae class Ia show no helium absorption in their spectra but show a strong absorption of singly ionized silicon atoms at about 610 nanometers; supernovae class Ib have helium lines, but no silicon lines and supernovae class Ic have neither; hydrogen is absent in all supernovae spectra type I. Supernovae spectra change significantly, varying in brightness, as the explosion synthesizes heavy elements, such as gold, iron and oxygen in the thermonuclear reactions.

Supernovae class II are rarer and show significant hydrogen absorption and are thought to collapse into a neutron star or Black Hole, having a pre-explosion mass of over 8 solar masses.

The brightest supernovae are of type Ia and the uniformity of their light curves allows calibration of their apparent brightness with their 'standard' true brightness, the luminosity so serving as an indicator as to their distance by astronomical distance-luminosity calibrations.

About one supernova class Ia explodes in a typical galaxy every 300 years, so in observing a large sample of about 3600 galaxies, one such explosion per month should be seen.

The experimental data collected by the various supernova observers, and under utility of the Hubble Space Telescope to track the brightness variations of discovered supernovae type Ia, now converged in 1998 to the conclusion, that distant supernovae are between 20% and 30% dimmer than expected and as a consequence of their measured redshift they appear to be further away than theory permits.
An interpretation of this discovery implies, that the universe's expansion is accelerating; the measured redshift depicting a distance further away for a dimmer brightness than anticipated by theory.

Closer analysis of the redshift data shows an expected distribution of luminosity, calibrated to their distances in the Chilean Cala-Tololo data, up to a redshift of about 0.11 and with a redshift-gap until a redshift of 0.3; after which the 'High-Z's' begin to show the 'curving away' from a predicted decelerating expansion rate in concordance with an Euclidean flat universe of Einsteinian General Relativity.

The highest redshift recorded in 1998 was that of 'supernova Iae' at (z=1.1) by the 'High-Z-Team'. Why is there a redshift gap between z=0.11 and z=0.30 approximately?

Does this imply a scarcity of supernovas in this redshift interval or is there a cosmological reason for this gap? Is this cosmological reason at the core of the Dark Energy implication and the 'factuality' of an accelerating universe?

This treatise shall elucidate the cosmological nature of Dark Energy and the inferred accelerating cosmology of an accelerating universe, stipulated to begin some 5-6 Billion years ago and as a change from a measured deceleration from light speed in the early universe.

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The stipulated 'Age of the Universe' of 14.2 Billion years corresponds to the latest measurement of the 'Hubble Constant' of the Planck Mission (2013-2018) for a more distant universe and a Hubble Constant of so 67.8 km/Mpc.s; but in discrepancy with measurements of about 74.0 km/Mpc.s for the nearby universe (Magellanic Clouds so 162,000 ly away {z=0.0093} NASA-ESA and Gaia Space Telescopes 2013-2019).

For a linear expansion H_o=c/R_max =1/Age of Universe and so gives 1000(3.26) ly/67.8 = 14.4 Gy for the Planck Mission and 1000(3.26) ly/74.0 = 13.2 Gy for the Gaia Space-Telescope.
Measurements in the nearby universe so infer a younger Age for the Universe and measurements in the universe further away imply an older Age of the Universe.
Is the nearby universe related to the 'Local Flow' for redshifts below a critical value, say related to the z=0.11 value measured for the apparent acceleration of the universe, caused by the negative pressure of the Dark Energy?

Indulge yourself in a thought experiment and travel with the expanding event horizon, the boundary of the universe (which has no boundary in the curved overall sense, all locations being centered self-relatively), this then becomes the looking back in time to the origin of the Big Bang.
You then experience the receding origin of the singularity slowly moving away from you and relative to you as 'stationary observer' at the event horizon, your own recessional velocity of (22% of (c)) is nullified and must be accounted for in your calculations of the recessional universe you are observing.
A description of the universe as decelerating with precise deceleration parameters given in a balancing of a gravitational omega, a quintessential lambda and a Milgrom parameter points to a possible variation in the Electromagnetic Fine-structure constant Alpha.
The Dark Energy crystallizes as a negative pressure however embedded as a quintessence in a multi-dimensional cosmology linked to the manifestation of 10-11-12 dimensional supermembranes.

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

and Λ = 0 from the formulation of General Relativity in Einstein's field Equations:

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for the Einstein-Riemann tensor

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and is built upon ten so-called nonlinear coupled hyperbolic-elliptic partial differential equations, which 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_criticalM_critical.c²/M_critical.c⁴ = 3H_o²Vcritical/c² = 3Vcritical/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 - Native 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.

The Friedmann equations for the Friedmann-Robertson-Walker FRW model for the field equations of General Relativity relate the dark energy pressure P to the matter density r(t) as an integrated part of a Lambda Cold Dark Matter LCDM model for the multidimensional cosmology for a flat Minkowski universe, albeit as an effect of the collocal interaction of a positively curved de Sitter dS universe with a negatively curved Anti de Sitter AdS universe.

The g_μνΛ = 8πG/c⁴ T_μν - G_μν cosmological constant-quintessence tensor becomes integrated as the difference between the Energy-Stress tensor 8πG/c⁴ T_μν and the curvature Einstein-Riemann tensor G_μν with negative pressure P(n,t) describing the matter density r(n,t) as a change in the time rate change of the Hubble parameter dH(n,t)/dt and therefore the change in the intrinsic Milgröm deceleration as a function of the nodal Hubble parameter.

Pressure P as an energy per unit volume Mc²/R³ is always negative and increases as a functional part of the dark energy defined as an Einstein quintessence L(n) towards its w=0 value for a matter dominated universe and can therefore be considered integrated as P < rc² as P = wrc² ∀ w<0

The derivative of the integrated pressure is defined in a maximum where the matter density M_oc²/R(n)³ is equal to a polynomial function native to the integrated pressure in L’_P(n) = n(2n+1)/[n+1]⁵.


Einstein Quintessence Integrated Dark Energy Pressure

Deceleration parameter

q(n) = -{(d²a/dt²)(a}/(da/dt)² for scale factor a = R(n,t)/R_H

Hubble Parameter

H(n,t) = (da/dt)/a with H(n=H_ot) = {c/[n+1]²}/{nR_H/[n+1]} = H_o/(n[n+1]) = H_o/T(n)
dH(n,t)/dt = {(d²a/dt²)/a – (da/dt)²}/a² = -q(n){(da/dt)/a}² - H(n,t)² = -H(n,t)²{1+q(n,t)}
dH/dt = -H_o²/(n²[n+1]²){1 + (2cH_o/[n+1]³)(nR_H/[n+1])([n+1]⁴/c²)} = -H_o²/(n²[n+1]²){1 +(2cnH_oR_H/c²)}
dH(n=H_ot)/dn = -{H_o/T(n)}²{1+2n} for q(t) = -(dH/dt)/H(t)² - 1 = 1+2n-1 = 2n for dS expanding within AdS

The AdS expansion has scale factor a = nR_H/R_H = n with invariant recession velocity c and 0 acceleration and is a function of n=H_ot limited in the Particle Hubble event horizon R_P(n) = T(n)R_H = n(n+1)R_H.

As the deceleration parameter will be q=2 for n=1 for the nodal Hubble boundary H_o for the dS-AdS spacetime mirror for the EMMI Lightpath a product q_AdS.q_dS = 2n(1/2n – 1) = 1 – 2n with a superposed deceleration parameter q_dS for the cyclic cosmology of the EMR Lightpath initializes the dark energy onset for n=½ to give the deceleration parameter product a zero value in q_AdS.q_dS = 1 – 2(½) = 0.
This then defines q_dS(n) = 1/2n – 1 generally and q_dS = -½ for q_AdS = 2 for the nodal Hubble bound n=1
For a present cycle time coordinate n=1.1327127.. q_AdS = 2.26542 and q_dS = -0.5586, the q_dS value being measured by astrophysical experiments.

Dark energy initiation for n=½ then occurs for q_AdS = 1 with q_dS =1/1 – 1 = 0
This stipulates a Hubble time (1.132712 - ½)/H_o = 0.632712/H_o = 10.677 billion years ago for the open AdS spacetime and a Hubble time (0.867288 - ½)/H_o = 0.367288/H_o = 6.198 billion years ago for the closed and compressed dS spacetime. The cosmological relativistic Doppler redshift is z_DE=0.6124 for a Cosmic radiation background temperature of 4.254 K*.

The compressed dS spacetime is spherically closed and embedded within a spherical dark matter inclusive AdS spacetime. The Riemann hypersphere as a 3-dimensional surface derivative of a 3-sphere of volume V₄(R) = ½p²R⁴ in dV₄/dR = 2p²R³ geometrically encompasses both interacting spacetimes in the horn torus topology coordinate shifted between the three frequency mirror intervals [-1,0] intersecting [-½,+½] intersecting [0,1].

These cosmic mirror-shifted Hubble horizons for the Light Energy universe and the Dark Energy shadow universe are then defined in an overall encompassing closed spherical universe defined by the Particle horizon of the expanding omniverse.

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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}} .................................[Eq.VII-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..............[Eq.VII-2]
{(d²a/dt²)/a} = -4πG/3{ρ+ 3P/c²} + Λ/3 ....................[Eq.VII-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 [Eq.VII-2] and substituting [Eq.VII-1] with [Eq.VII-2] gives [Eq.VII-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 and with a cancelling integrated cosmological constant Λ/3 in derivative dH/dt

{(d²a/dt²).a - (da/dt)²}/a² = -4πG{ρ+ P/c²} + (kc²/a²)
for (kc²/a²) = 8πGρ/3 - H² + Λ/3 = 0 for integrated Λ/3 = 0 and ρ_critical


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)


Scale factor modulation at N_k={[n-∑∏n_k-1]/Πn_k } for R(n)_dS = ½R(n)_AdS for n=1, k=0
{dH/dt} = d{H_o/T(n)}/dt = - H_o²(2n+1)/T(n)² for k=0 and n_-1=0 and n_o=1

dH/dt + 4πGρ = - 4πGP/c² for integrated Pressure P(t) = -(dH/dt)/4pG - r (t)
G_or = G_oM_o/R(n)³ = -G_oP/c² – (dH/dt)/4p = L(n)/R(n) + 2cH_o/R(n)[n+1]³ for Volume V_dS = 4pR(n)³/3

-P(t) = {c²/G_o}{L(n)/R(n) + 2cH_o/R(n)[n+1]³ + (dH/dt)/4p}
= {c²/G_o}{L(n)[n+1]/nR_H + 2H_o²/n[n+1]² – H_o²(2n+1)/4pT(n)²} P(n=H_ot) ={c²H_o²/4pG_oT(n)²}{2n+1-8pn+8pn} – M_oc²/R(n)³= c²H_o²(2n+1)/4pG_oT(n)²} - M_oc²/R(n)³

P(n=H_ot) = c²H_o²(2n+1)/{4pG_oT(n)²} - M_oc²/R(n)³ for the spherical V_dS = 4pR(n)³/3
P(n=H_ot) = c²H_o²(2n+1)/{6p²G_oT(n)²} - M_oc²/R(n)³ for the hyper-spherical V_dS = 2p²R(n)³

P(n,t) < 0 for an integrated Pressure coordinate maximum for the interval [n_ps---0] for [-3x10¹³⁴---]
M_oc²/R(n)³ = c²H_o²(2n+1)/{4pG_oT(n)²} for R_H/2pR_sarkar = M_H/2pM_o = [n+1]⁵/[2n²+n] = 1/L_P(n)

for 2pW_o = 0.176117… = L_P(n) = [2n²+ n]/[n+1]⁵ = n[2n+1]/[n+1]⁵ for Volume V_dS = 4pR(n)³/3
for 3p²W_o = 0.829935… = L_P(n) = [2n²+ n]/[n+1]⁵ = n[2n+1]/[n+1]⁵ for Volume V_dS = 2p²R(n)³

P(n=n_ps) = -3x10¹³⁴ for L_P(n) = n_ps = l_ps/R_H = 2pr_ps/R_H = 6.2590935x10^-49 for k=1 universe reset r_psYⁿ = R_H for cycle reset coordinate n_reset = ln(R_H/r_ps)/lnY = ln(2p/n_ps)/0.48121146 = 234.4715

P(n=n_ps) = -3x10¹³⁴ [J/m³]* for L_P(n) = n_ps = 6.2591x10^-49
P(n_Lo=0.1083) = -2.3761x10^-8 [J/m³]* for L'_P(n) = 0.078793
P(n_LPmax=0.40825) = -3.939x10^-9 [J/m³]* for L'_P(n)=0.13389451796
with 2pW_o = 2pM_o/M_H = 4pG_oM_o/c²R_H
P(n_DE=½) = -2.7264x10^-10 [J/m³]* for L'_P(n) = 0.13168724…
P(n_Ho=1) = -1.4976x10^-10 [J/m³]* for L'_P(n) = 0.0937500
P(n=1.132712) = -1.4004x10^-10 [J/m³]* for L'_P(n) = 0.0938113…
P(n=234.4715) = -4.0541x10^-11 [J/m³]* for L'_P(n) = 1.5221x10^-7

For L(n=n_ps=|l_ps/R_H|_mod) = G_oM_o/l_ps² = 2.015x10⁸⁵ [m/s²]* and n_ps=l_ps/R_H as min-max scale boundaries
→ P(n,t) = M_Hf_ps²/R_H{1/2p – W_o/n_ps} = 3.645x10⁸⁷{1/2p - 4.478x10⁴⁶ [N/m²]* O{-3x10¹³⁴}< 0
for a spherical V_dS= 4pR(n_ps)³/3 = 1.029x10^-144 [m³]* and for a boundary and initiation redshift z~2x10²⁴ of the instanton-inflaton QBBS

For L = 0 the onset of the Einstein quintessence changing from positive to negative for n=0.10823
L(n_DE)(R(n_DE) = (1073.61)G_oM_o/R_H³ – (84.56)H_o² = (5.3053 – 5.3053)x10^-35 [1/s²]* for a negative Einstein quintessence of 0 [1/s²]* for L(n_DE) = {8.2774 - 8.2774x}10^-10 = 0 [ms^-2]*
→ P(n,t) = c²H_o²(1.21646)/{4pG_o(0.01439)} - M_oc²/R(n)³ = (1.9212–4.2973)x10^-8
= -2.3761x10^-8 [N/m²]* for the spherical V_dS = 4pR(n)³/3 [N/m²]*

For L'_P = 0 the integrated negative pressure maximum coordinate for M_oc²/R(n)³ = L'_P(n)=0.40825 for the derivative of L'_P(n)=(2n²+n)/[n+1]⁵ = 0.13389451796 for d{L'_P(n)}/dn = 0 for L”_P(n) = (4n+1)/[n+1]⁵ - 5n(2n+1)/[n+1]⁶ = 0 for n=1/√6 = 0.40825

Showing that the Pressure P would be 0 for this coordinate were it not integrated in the Lambda tensor
L(n_DE)(R(n_DE) = (41.04504)G_oM_o/R_H³ – (2.47027)H_o² = (2.0282 – 8.70985)x10^-36 [1/s²]* for a negative Einstein quintessence of -6.68165x10^-36 [1/s²]* for L(n_DE) = {9.3941 – 40.3402}x10^-11 = -3.0946x10^-10 [ms^-2]*
→ P(n,t) = c²H_o²(1.8165)/{4pG_o(0.33053)} - M_oc²/R(n)³ = (1.2490–1.6429)x10^-9
= -3.939x10^-9 [J/m³]* for the spherical V_dS = 4pR(n)³/3 [N/m²]* as the Lambda integrated pressure at 6.891 billion years after the QBBS as P(n=0.40825) to define a maximum 2pW_o=2pM_o/M_H in the baryon matter seedling

For the onset of dark energy for deceleration parameter product q_AdS.q_dS = 2(½)(1/1-1) = 0 for n=½
L(n_DE)(R(n_DE) = (27)G_oM_o/R_H³ – (8/9)H_o² = (1.3342 – 3.1341)x10^-36 [1/s²]* for a negative Einstein quintessence of -4.9339x10^-36 [1/s²]* for L(n_DE) = -2.6276x10^-10 [ms^-2]*
→ P(n,t) = c²H_o²(2)/{4pG_o(9/16)} - M_oc²/R(n)³ = (8.0807–10.8071)x10^-10
= -2.7264x10^-10 [N/m²]* for the spherical V_dS = 4pR(n)³/3 [N/m²]*

For the nodal Hubble constant H_o for n=1
L(n_DE)(R(n_DE) = (8)G_oM_o/R_H³ – (16/9)H_o² = (3.9532 – 6.2682)x10^-36 [1/s²]* for a negative Einstein quintessence of -2.3150x10^-36 [1/s²]* for L(n_DE) = -1.2329x10^-10 [ms^-2]*
→ P(n,t) = c²H_o²(3)/{4pG_o(4)} - M_oc²/R(n)³ = (1.7045–3.2021)x10^-10
= -1.4976x10^-10 [N/m²]* for the spherical V_dS = 4pR(n)³/3 [N/m²]*

For the present time n=1.132712
L(n_present)(R(n_present) = G_oM_o/R_H³(n/[n+1])³ – 2nH_o²/T(n)² = (3.2984 – 13.686)x10^-37 [1/s²]* for a negative Einstein quintessence of -1.08387x10^-36 [1/s²]* for L(n_present) = -8.8143x10^-11 [ms^-2]*
→ P(n,t) = c²H_o²(3.2654)/{4pG_o(5.8358)} - M_oc²/R(n)³ = (1.2713–10.8955)x10^-10
= -1.4004x10^-10 [J/m³]* for the spherical V_dS = 4pR(n)³/3 [N/m²]*

For the quantum tunneling of the asymptotic protoverse into the first universe for n=234.4715
L(n_present)(R(n_present) = G_oM_o/R_H³(n/[n+1])³ – 2nH_o²/T(n)² = 5.0051x10^-38–5.4241x10^-43 = O(5x10^-38) [1/s²]* for a positive Einstein quintessence of 5.0051x10^-38 [1/s²]* for L(n_{quantumtunnel}) = 7.9624x10^-12 [ms^-2]*
→ P(n,t) = c²H_o²(469.943)/{4pG_o(3.0483x10⁹)} - M_oc²/R(n)³ = (3.5037x10^-17–4.0541x10^-11
= -4.0541x10^-11 [N/m²]* for the spherical V_dS = 4pR(n)³/3 [N/m²]*

As G_oM_o=G(n)XⁿM(n)Yⁿ=constant with W_oYⁿ=W_BM G_oXⁿ.YⁿW_o = G(n)W_BM for 2pW_o- L_Pmax(n=0.40825)
1 + 2pW_o – L’|_max = G(n_measured)/G_oXⁿ + d = W_oG_mYⁿ/W_BMG(n) + d for a measured G_m = G(n_measured)
1+0.176117-0.1338945 + d = 1.0422225 + d = {0.02803Yⁿ/0.04834}Yⁿ{G_m)/G(n) = 1.00009{G_m/6.442195x10^-11} for a monopole derived delta d = 1.0422225 – 1.035428 = 0.006794 G_m= 6.4416152x10^-11 {1.042225 + d} =6.6698x10^-11[m³/kg.s²]* and 6.67443x10^-11 [m³/kg.s²]_SI

The Dark Energy and the 'Cosmological Constant' exhibiting the nature of an intrinsic negative pressure in the cosmology became 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.
The encompassing cosmology so is always matter dominated in the sense of the overall energy distribution and the asymptotic zero approach of the integrated negative pressure quintessence.

Critical Density r_c = 3H_o²/8pG_o dS with r_c = H_o²/4p²G_o AdS in factor 3p/2

for H(n)² = {da/dt}²/a² = {c²/[n+1]⁴}/{n²R_H²/[n+1]²} = H_o²/n²[n+1]² = H_o²/T(n)²
for {da/dt}² = 8pG_or_ca²/3 dS and {da/dt}² = 4p²G_or_ca² AdS for spherical closure dS in omnispace as a function of the Particle Hubble event horizon of the nodal cosmology for critical density r_critical and curvature radius R_curv = 2G_oM_H/c² and scale factor a(n,t)=R(n,t)/R_H

∫da/a = ∫√{8pG_or_c/3}dt dS and ∫da/a = ∫√{4p²G_or_c} dt AdS
for ln{a} = √{8pG_or_c/3}t dS and ln{a} = √{4p²G_or_c}t AdS

for a(t) = exp[√{8pG_or_c/3}t] = exp[H_o] dS and a(t) = exp[√{4p²G_or_c}t] = exp[H_o} AdS

This correlates with a generalised density r(n=H_ot) varying cosmology, often modelled as a flat matter only de Sitter universe
with scale factor a(n,t) = R(n)/R_H = R(n)H_o/c ∝ t^⅔

H(n) = {(dR(t)/dt)/R_H}/{R(t)/R_H} = √{8pG_or(n,t)/3} = √{8pG_o(M(n,t)/3R(n,t)³} dS and
H(n) = {(dR(t)/dt)/R_H}/{R(t)/R_H} = √{4p²G_or(n,t)} = √{4p²G_o(M(n,t)/R(n,t)³} AdS
For √R(t).dR(t) = √{8pG_o(M(n,t)/3}.dt dS and √R(t).dR(t) = √{4p²G_o(M(n,t)}.dt AdS
For ⅔R(t)^1.5 = √{8pG_o(M(n,t)/3}t and R(t) = ∛{6pG_o(M(n,t)} t^⅔ dS and for ⅔R(t)^1.5 = √{4p²G_o(M(n,t)}t and R(t) = ∛{9p²G_o(M(n,t)} t^⅔ AdS within the closed dS omniverse

For AdS encompassing the cyclic dS protoverse as a multiverse as a closed dS spacetime, the scale factor is a=n=H_ot for dn/dt=H_o for the Particle Horizon and closure n=1 for M(n,t)=M_H=R_curvc²/2G_o with
nR_H=R(n,t) = ∛{6pG_o(M(n,t)} [n/H_o]^⅔ dS for nR_H³ = {6pG_o(M(n,t)/H_o²} = 9M(n,t)/4r_c and n = 9M(n,t)/4r_cR_H³ = {9M(n,t)/4R_H³}{4pR_H³/3M_H} = 3p{R_curv/R_H} = 3p for M(n,t) = M_H and n=1

For the dS omniverse encompassing the cyclic dS protoverse as a multiverse as AdS spacetime in the topology of a horn torus, the scale factor is a=n=H_ot for dn/dt=H_o for the Particle Horizon and closure n=1 for M(n,t)=M_H=R_curvc²/2G_o with
nR_H=R(n,t) = ∛{9p²G_o(M(n,t)} [n/H_o]^⅔ dS for nR_H³ = {9p²G_o(M(n,t)/H_o²} = 9M(n,t)/4r_c and n = 9M(n,t)/4r_cR_H³ = {9M(n,t)/4R_H³}{2p²R_H³/M_H} = 9p²/2 for M(n,t) = M_H and cycle n=1
The time for closure so becomes about one third the Hubble time 1/H_o = R_H/c in t² = R_H³/6pG_oM_H = R_H/3pH_o²R_curv = 1/3pH_o² for a time t=1.73473x10¹⁷ s* or n=0.32573 or 5.4971 Gy, when R(t=n/H_o) = 3.9253x10²⁵ m* = 0.2457R_H

For a present measured deceleration parameter q_dS=-0.5586, the DE Lambda as the negative Einstein quintessence calculates as -8.8143x10^-11 [m/s²]*or as 1.0388x10^-36 [s^-2]* and as a negative pressure of -1.4004x10^-10 [N/m²=J/m³]* as a function of the native universal Milgröm deceleration a_mil = -2H_o²R_H/[n+1]³ = -1.1614x10^-10 [m/s²]*.

The Einstein Lambda then becomes 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.

For W(n) = M(n)/M_H = 2q_o = 1 = R(n)/R_H the AdS cosmology attains closure for a cycle coordinate n=1 in the EMMR Lightpath and a time, when the dS gravitationally retarded universe has reached the halfway point in its asymptotically defined expansion in scale factor R(n,t)/R_H = n/[n+1] = a(n,t) in a recessional velocity of the expanding dS wavefront slower than the speed of light.

The dS compressed universe has reached the halfway marker for the onset of the dark energy at a cycle time coordinate of n=1 and when the AdS dark matter inclusive universe has reached the nodal Hubble event horizon as the boundary for the multidimensional cosmology as set in the superluminal Lightpath of the QBBS superimposed onto the parallel evolution of the dS and AdS spacetimes expansion.

The extent of the EMMR Lightpath in AdS so encompasses a full nodal displacement in the interval [n_ps~0,1] which is phase shifted as the interval [-½,+½] to mirror the invariance of the EMR Lightpath relative to the gravitationally retarded EMR Lightpath in the cycle coordinate n=½ as a proxy nodal mirror for the true Hubble node at n=1.
The ‘return’ of the reflected EMMR Lightpath from the true Hubble event horizon so is made manifest as the EMR Lightpath at the proxy Hubble node at the DE n-cycle coordinate n=½ and for which the deceleration parameter product is zero for q_AdS = 2n = 1 and q_dS =1/q_AdS – 1 = 0.

The actual curvature radius for n=½ for the dS cosmology is R(½) =½.⅔R_H = ⅓R_H to indicate that the dark matter portion for the compressed spacetime will be 1/2³–1/3³ = 1/8 – 1/27 = 19/108 = 0.0880 = 1/11.36 in terms of the volume occupied.
For n=1, the dark matter sector so will be doubled to 0.1759 = 1/5.6842 for the ratio between the dS sector without the dark matter and the AdS sector with the dark matter with 1/6.6842 + 5.6842/6.6842 = 1 or as so 15% BM and 85% DM as the total matter content of the universe.

The distribution for the present scale factor of 0.53RH gives W_BM = W_oY^1.132712 = 0.04834 and with n_present W_DM = W_o{1 + 1/n}³ = 0.2743 as 4.834/32.262 = 14.98% and 27.43/32.262 = 85.02%.

The difference between the AdS curvature radius for n=1 superposed onto the dS curvature radius for n=1 and the actual dS curvature radius for n=½ then is (½-⅓)R_H = ⅙R_H for a ratio of ½R_H/⅓R_H = 3/2

The density parameter W = R(n)/R_H = 1 so triggers the second universe from the lightspeed invariant AdS completion of the Lightpath in the AdS cosmology with the Dark Energy manifesting in potential energy vortices of wormholes defined in the inflaton hyperspace cosmology and superpositioned as the phase shift of the [n_ps,1] interval in the interval [-½,+½] as the dark energy onset.

This defines the Dark Energy onset for the difference between the AdS EMMI ct=nR_H Lightpath and the dS EMR expansion R(n)=nR_H/[n+1] as R_H{n – n/[n+1]} = R_H{(T(n)-n)/[n+1]} = n²R_H/[n+1] = ⅙R_H for n=½

This difference is trivially 0 for the QBBS and n=0~n_ps and is 0 for the intersection coordinate for the stasis of the dark matter part with the baryonic matter part of the energy density for the cyclic return of the EMMI Lightpath ct=R_H{2-n} > R_H with {2-n}=n/[n+1] or 2-n² = 0 for n_BMUDM = √2
For n=1 and the nodal Hubble event horizon the AdS-dS difference n²R_H/[n+1] = ½R_H for=n/[n+1]

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

This cosmological analysis of the phenomena predicts, that supernovae type Ia with a redshift above 1.84 will be measured to conform to the theoretical predictions for a decelerating and flat super cosmos. The appearance of an accelerating cosmos is a limited phenomenon, relevant for a specific and unmapped redshift interval from (z=0.343 to 0.291), with interval (z = 1.080 to 1.840) imaged in the interval (0.343 to 0.291) with a variation maximum for the mapping at the Arpian limit (z_arp = 0.25045).

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

The 'de Broglie' inflationary model, where a supermembrane epoch ends in time instantaneity as the EpsEss heterotic superstring, which then expands with a decreasing recessional velocity towards a 'de Broglie' boundary as macro-quantization in 10D, but beginning with light speed (c) under guidance of Special Relativity can be applied.
Other inflation scenarios, such as chaotic inflation had proved untenable by the experimental data and the microwave background pointing to a zero curvature and to a flat universe.

The macro quantization of the heterotic superstring, also known as HE(8X8) constitutes the 'conifolding' of the higher dimensions, either as a 6D-Calabi-Yau manifold or as a 7D-Joyce-Sphere, relative to 10D-C-space and 11D-M-space respectively.

https://arxiv.org/pdf/astro-ph/9805201.pdf​

And the 'de Broglie' inflation quantizes Einstein's field equations of General Relativity in their Friedmann formulations; the Milgrom parameter becoming acceleration: {d²r(n)/dt² = -2cH_o/(n+1)³} and the distance-scale factor parametrizing as: {r[n] = R_max(n/(n+1))} and the velocity as: {dr(n)/dt = c/(n+1)²}; the parametric constant for dimensionless cycle time is: (n = H_ot for dn/dt = H_o).

And so knowing the present cycle time (n_p=1.1327117) via an arbitrary Mean-Alignment-Time or MAT, relative to a phase shifted proto universe and set as (Midnight, November 4th, 1996, Canberra, Australia, local time); the present universal speed of recession is calculated as 0.2198c or (22% of c), which then maps a self-relative 'Arpian redshift' as the renormalization for the receding event horizon, mirrored in the Big Bang singularity; (z_arp = 0.25045).

We also calculate the 10D expansion of the universe as (53.111% or a radius of 8.963 billion lightyears), increasing to (113.27% or 19.12 billion lightyears [ly]) for the 11D universe.
The Hubble-Oscillation so defines the nodal Hubble-Constant: (H_o=1.877728045x10^-18 1/s*) or 58.04 Hubble Units [km/Mpc.s]) and the 10D-cosmic asymptotic diameter as (33.752213 billion ly*). The Hubble constant varies between f_ps and H_o as H_o.R_H = λ_ps.f_ps = c and is calculated to assume a value of 66.9 Hubble units for the present time coordinate n_p in the cosmic evolution.
The Alpha-Variation so encompasses a period of (2[19.12 - 16.88] = 4.48 billion years) and hence two distance intervals; one from the present epoch (n_p) to a distance 2.24 billion years into the past at the nodal value (n=1) and its 11D-image at (n=1-0.13271...=0.867289).

Relative to the Big Bang Source however, this interval is mapped from (n=0.13271... to n=0.26542...) as a linear double interval; just as two mirrors facing each other would reflect each other in the spacetime 'in between'. This 'in between' becomes our expanding spacetime and we can calculate the relevant distances, using cycle-time n as parameter and the nodal Hubble-Constant as invariant at (n=1).

At (n=0.13271...or 2.24 billion years after the Big Bang; v'/c=0.77940 and z =1.840), relative to the nodal Hubble event horizon and at (n=0.26542... or 4.48 billion years after the Big Bang; v'/c=0.62449 and z =1.080), relative to the nodal Hubble event horizon.
The cosmological redshift epoch between (z=1.080 to 1.840) and corresponding to a 2.24 billion year duration includes the 'peak of galaxies' at (z=1.18) and is characterized in the absolute minimum of the quintessential lambda and the gravitational maximum contractions to form galactic structures and superstructures under the auspices of the Sarkar Constant of 236.1 million lightyears.

Now looking back at those large redshift values, the lower one coinciding with the redshift of z=1.1 for supernova 1998 Iae, measured by Brian Schmidt of the 'High-Z-Team' must encompass a 'looking through' the imaged z-interval, namely the interval from the node at 2.24 billion years back to 4.48 billion years or the z-interval from (n=0.86729, v'/c=0.28680, z=0.343) to (n=1.0000, v'/c=0.2500, z=0.2910).

In other words, the 11D intersection of M-space intersects 10D-C-space in the two intervals, which form self-relative images of each other.
The 10D Riemann hypersphere is subject to gravitation in mass-parameters and decelerates asymptotically towards its 11D M-space boundary in negative and open curvature, mirroring the asymptotic expansion in perfect flatness of Euclidean zero curvature, however.
The EMR-parameters so double themselves in the said interval, an interval which is itself expanding and contracts between the two nodal values of maximum frequency (f_ps) and minimum frequency (H_o).

But it is only the EMR parameter that defines this 'oscillating universe', the mass parameter remains asymptotic as defined in the parametric scale factor {r(n)=R_max(n/(n+1), with R_max = R_Hubble = R_H = 1.59767545x10²⁶ m*}.
Revisiting the redshift data of 1998, we notice the 'missing redshifts' in the interval from (z=0.11-0.3), with the limiting nodal (z=1.840) mapped onto the nodal (z=0.291) and the boundary image (z=1.080) mapped in its boundary image (z=0.343). The first supernova, beginning to 'curve away' from the decelerating expansion predicted by theory, is at about (z=0.11).

​

Any receding cosmological object with a redshift exceeding (z=0.291) can be considered to be moving in the 'Hubble Flow' with a measured redshift (z_m=z), because after a distance of 2.24 billion ly no doubling of the electromagnetic parameters occurs for the distance between the two cosmic nodes.
But we find three z-intervals, in whom we must apply a redshift-correction; set in the images of the boundaries and the nodes. The fixed odd (1,3,5,...) Hubble Node H_o for Protoverse (k=0 in a Multiverse cosmology in parallel time space, but collocal in spacetime:
(https://cosmosdawn.net/attachments/article/29/mathimatia10.pdf )

is imaged in a unitary interval {n: n_ps-½-1} and across the Dark Energy Mirror at n=½ in the even (0,2,4,...) Hubble Node of the Big Bang for

n_ps=λ_ps/R_Hubble=(c/R_Hubble)/(c/λ_ps)=H_o/f_ps=6.259...x10^-49.
​

The odd node remains fixed in the multiverse but allows a transversion of the electromagnetic speed-invariant light path to oscillate between the two nodes in a lower dimensional, say 10D stringed cosmology. The 11D light path so is both reflected into this 10D string space, but also continues into 11D membrane space in the creation for the multiverse generations in a resetting and extension of the initializing parameters of the Big Bang defining the protoverse.
The reflected 11D light path so intersects its own journey from the Quantum Big Bang (qbb), once the first odd node H_o has been encountered so 16.876 Billion years following the qbb genesis.

This implies that a second universe for k=1 is generated as soon as the first universe, initiated as k=0 has attained a full covering of the Hubble Event Horizon, set by the Inflaton.
A second universe, collocal with the first universe so was created in a second qbb 19.115-16.876=2.239 Billion years ago.
As the spacetime for k=0 was created by the first Inflaton, the second universe became superimposed onto the first, already existing universe in a multi-dimensional spacetime defined by the 10D-closed cosmology of de Sitter positive curvature, albeit expanding as a 11D-open cosmology of Anti-de Sitter negative curvature.

At the critical node (n=1) the positive gravitational pressure from the perspective of a present day cosmological Earth-Time observer, measuring the universe backwards in time for increasing cosmological redshifts - is balanced by a negative Dark Energy pressure from the perspective of a relative present day Big Bang Genesis observer, measuring the universe forwards in time for increasing cosmological redshifts.
A superposition of the two self-relative observers, then cancels the curvatures to result in an overall Euclidean-Minkowskian flat cosmology. This congruence or qbb entanglement so enables the origin of the Dark Energy to derive from a quasi-negative spacetime, here termed as a Shadow Universe Khaibit.
Khaibit so expands spacetime from its own singularity contraction of no space and no time as given by the Instanton parameters of supermembrane E_psE_ss.

​

This 'singularity interval' so is a collocal point space in the Shadow Universe and is defined by the boundary value of the redshift of the string space, given by the n-coordinates of the oscillating de Sitter cosmology.
In the Anti-de Sitter cosmology of the refracted-continuing 11-dimensional light path, the light path defines the multivalued coordinates for the Hubble Node oscillation within the unitary interval as given by kth universe embedded within the omniverse.
The entirety of space in any multiverse, so can be considered as a 'singularity point space' relative to Khaibit, the Shadow Universe, containing or embedding within its higher dimensional extent lower dimensional or compressed-conifold spacetime.

The boundary (z_arpimage=0.343, z_node'=1.080) is imaged as the 10D-boundary image (z_arp=0.25045) in the 10D-nodal mirror of (z_node=0.291, z_arpimage'=1.840) and the present 11D-boundary mirror of (z_arp=0.25045, z_BigBang~10²⁴) images the Big Bang-0D-10-11D 'singularity point space' in the shared nodal 10D-11D-boundary (z_arp=0.25045).

If (v'/c=0.22), then (z_m=z_arp=0.25045 as the variation maximum) and at the event horizon, where z_m=0, the z(z_m)=z_arp and az_m+b=0.291 for z_m=z_{nodalintersection}=z_ni; subsequently (b=z_arp & az_ni=0.04055) and a the gradient of the 'Local Flow', given in the equation: z(z_m)=az_m+0.25045 for the present epoch.

The intersecting redshift interval for the present time spans the z(z_m) range from (0.291 to 0.343) for the z_m-interval from (z_ni to 0.25045) with positive gradient (0.343-0.291)/(0.25045-z_ni)=(0.052/(0.25045-z_ni) and letting this gradient define the intersection of z_node=z_m=z_ni and where z(z_m)=z_m(n) for z_red(z_m) = 0.37045(z_m) + 0.25045 = 0.291 = z_node gives z_ni=0.10943 for gradient (0.34323-0.25045)/0.25045 = 0.09278/0.25045 = 0.37045, so defining the

Redshift-Correlation-Equation: z_red(z_m) = 0.37045(z_m) + 0.25045

The intersecting blueshift interval for the present time spans the z_m-interval from (0.25045 to 0.29099) for the same range with a negative gradient (0.34323-0.29099)/(0.25045-0.29099)=-0.05224/0.04054=-1.2885) and a linear Blueshift-Correlation-Equation:

z_blue(z_m) = -1.28804(z_m) + 0.666 = Cosmological Blueshift Region

Then the 'curving away' from the deceleration model at (z=1.11) becomes a consequence of the redshift (z_ni=0.10943) forming a nodal image from positive space in negative space to indicate redshift coordinates below the boundary coordinate given by zarp = 0.25045 as the redshift of the universes expansion for the age of the universe determined by the speed of recession (v) of its 11-dimensional surface boundary by n = √{c/v} - 1 = √{1 + 2/(z²+2z)} – 1

The relativistic redshift formula suffices, because the expanding space of the universe in the Instanton is parametrically set by the Inflaton as the light path for the nodal Hubble oscillation - poetically called as the 'Heartbeat of the Mother Universe' or the 'Breath of Baab Universe' within the 'Breath of Abba Khaibit. The Hubble Law Hubble Constant = Recessional Velocity/Distance or H = v/D = constant is used to estimate the cosmological distances. The cosmological redshift so is comoving with the recessional velocity given by v/c and the redshift z= v/c as a proportion of lightspeed c for a recessional velocity v is approximately linear for z<1 and so the Local Flow as distinct from the Hubble Flow here considered.

The true 'Hubble-Flow' so begins at z_m = z_node = 0.291 in the present epoch with linear equation: z(z_m) = z_m.

​

R_ps = λ_ps/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 = M_pL_p = M_psR_ps.
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.

The quantum gravitational mass M_hyper = ½{R_ps/L_p}². m_ps then could evolve as M_hyper.Yⁿ = M_H in cycle time n=H_ot and in the form of the Black Hole masses or equivalently in the form of the wormhole radius R_ps expanding to the size of the Hubble event horizon R_H=2G_oM_H/c₂ as the Inflaton boundary in the higher dimensional spacetime.
Solving for the completion of the protoverse in n-cyclicity then gives n = ln{M_H/M_hyper}/lnY =ln{R_H/R_ps}/lnY = ln{1.47325..x10²⁵}/ln{1.618034} = 234.471.. and indicating that 234.471 half-oscillations of the Hubble parameter between its minimum Instanton node and its maximum Inflaton node would be required to expand the wormhole radius of the Instanton and hypermass M_hyper to the Hubble event horizon as the 11-dimensional boundary of Klein.

As one-half cycle of the 'Heartbeat of Mother Universe' requires 1/H_o= R_H/c = 5.32558..x10¹⁷ s* or so 16.876 Billion years; the evolution of the protoverse as the seed for phase shifted multiverses within the Omniverse would take 234.471x16.876 = 3.957x10¹² years.
After about 4 Trillion years then, the protoverse would quantum tunnel into the next iteration of its Mathimatia definition and a second universe which would have been created by a resetting of the initializing parameters of its precursive first universe or protoverse.
And so the second Inflaton became triggered when the light path of the first universe had reached the Hubble node of the first Inflaton 16.876 Billion years from the beginning of the protoverse.

After trillions of years the first evolution of the mass seed in Universe would have exhausted the transmutation of the elements in the birth and death of stars and galaxies and the Omniverse would require a 'recharging' of the mass seed from the VPE as the energy reservoir of Abba in the physical cosmology.
As universal energy quantum of potential physical manifestation from nowhere in notime this potential energy remains unlimited and the Omniverse in spacetime cannot exhaust its VPE from which the physicalized energy emerges.

At the Inflaton boundary, the 11-dimensional light path in the invariant light speed parameter 'c' in the higher dimensional universe had been both refracted into the 11th dimension, creating new spacetime in the second universe as a multiverse and it had been reflected back into the lower dimensional universe.
At the Inflaton boundary, the 11-dimensional light path in the invariant light speed parameter 'c' in the higher dimensional universe had been both refracted into the 11th dimension, creating new spacetime in the second universe as a multiverse and it had been reflected back into the lower dimensional spacetime as an EMR-EMMR coupled parameter in a 'deja vu' visitation of the 10-dimensional spacetime.
This 'return of the light' would self-intersect the expansion of Universe and define particular values for the comoving reference frame for bilocated cosmic or universal observers, one at the origin of the Instanton and the other comoving with the 10-dimenmsional boundary of the Instanton as the image of the Inflaton event horizon.

Particular cosmological redshift corrections would have to be applied to account for this self-intersection of the multi-dimensional light path to avoid the measurement of this light path as a relative blueshift of approach to be considered a redshift of recession and to presume an accelerating universe apart from the natural acceleration caused by the Dark Energy from Khaibit in balancing the natural Milgröm deceleration of the cosmogenesis with the gravitational pressure of the baryon seed M_o.

M_o so evolves as the luminous or baryon matter seed from the baryon part of M_H defined in Ω_o=M_o/M_H = 0.02803 from the Instanton. At the beginning, 2.8% of Universe's mass content was baryonic-luminous and would increase as a function of M_oYⁿ until the Instanton in an 'open' 10-D spacetime of 'de Sitter' dS would intersect the 'closed' 11-D spacetime of 'Anti-de Sitter' AdS for a n-cycle coordinate n_DM∩BM = √2 and when the return of the EMR-EMMR light path would be imaged in the n=0.58578... coordinate specifying the forward journey of the light path from the Instanton 9.894 Billion years from the time of the birth of the physicalized universe.

The baryon seed would then constitute 5.536% of the total mass energy and remain constant at that value. The Baryon Matter BM would so be embedded in the Dark Matter DM and both would be encompassed by the Dark Energy DE in terms of the mass energy of the Universe. Now it would require a precise half cycle for the Hubble oscillation to calibrate the lower 10D-expansion with the higher 11D-expansion of the light path in the scale factor R(n=½) = R_H{n/(n+1)} = ⅓ R_H for a full cycle of n=1 for the 11-dimensional invariant light path speed to reach the Hubble event horizon in R(1) = R_H{1/(1+1)} = ½R_H.

The gravitationally decelerating universe had expanded to a size 1/27th of the volume of Universe as a Mother Black Hole at a cycle time 0f 8.438 Billion years, when the DE began to appear as an inertia associated parameter in Universe. It was at this n-cycle coordinate, that the Dark Energy became initiated as a function of mass seed M_o , which as a potential energy form of the VPE/ZPE, had been awaiting light path 'c' to 'illuminate' or to trigger this potentiality.

Until that time the DM component had made up the difference to the BM in BM+DM = 1. The DE in the de Sitter spacetime had been 0 as a function of mass, but it had been and continued to be the balance between the dynamics of the gravitational baryon mass seed and the inherent cosmological Milgröm deceleration as a quintessence.

The nearest, most studied, and most luminous quasar (or quasi-stellar object) is called 'Q3C273' (Cambridge catalogue); its recessional velocity is measured as (v/c=z_m=0.1583).
Quasar-Blazar-ActiveGalacticNucleus Q3C273 is located in the constellation of Virgo and its distance D, using the Hubble Law is D = zc/H.

For a (Planck Mission) Hubble Constant of 67.8 Hubble units D = zc/67.8 = 0.1583c/{67.8/(3.0857x10¹⁹)} = 2.164x10²⁵ m* or 2.28 Billion ly.

For a (ESA-NASA) Hubble Constant of 74.0 Hubble units D = zc/74.0 = 0.1583c/{74.0/(3.0857x10¹⁹)} = 1.9804x10²⁵ m* or 2.09 Billion ly.

Using the present calibrated Hubble Constant H(n_p) = H_o/(2-n_p) = (58.04 km/Mpc.s)/0.86729 = 66.92 km/Mpc.s
D_Q3C273 = 0.1583c/(66.92 [km/Mpc.s]*) = 0.1583c/{66.92/(3.0857x10¹⁹)} = 2.1898x10²⁵ m*= 2.313x10⁹ ly = 709.75 Mpc and where 1 parsec (pc) = 3.0857x10¹⁶ m* or 3.259 lightyears.

Distance D for the nodal Hubble parameter yields D_node = (66.92/58.04)D_Q3C273 = 2.5250x10²⁵ m* = 2.667x10⁹ ly = 818.34 Mpc

Increasing the applied value for H from its nodal value so decreases the calculated distance to the Quasar.
But this redshift z_3QC273 is not in the Hubble Flow and must be corrected by n_Q3C273 = √{c/v} - 1 = 2.5134 - 1 = 1.5134 and for a n-cycle time coordinate exceeding that of the boundary value of n_present = 1.1327117...in the second Hubble semi-cycle in the 'electromagnetic 11D-return' of the light path.

Applying the Alpha-Redshift equation z_red(z_m) = 0.37045(z_m) + 0.25045 gives a 'local flow correction' of: (z(0.1583)=0.30909), for which {v'/c=(z²+2z)/(z²+2z+2)=0.2630} = {1/(n'+1)²} for a corrected n'=√(1/0.2629) - 1 = 0.94993

The position of Blazar Q3C273 is therefore 1.1327117-0.94993 = 0.18278 n-units from the n_present cycle coordinate at a linear displacement of 2.920235x10²⁵ m* or 3.0846 Billion ly from n_p within the Local Flow, but not in the Cosmological Blueshift Region, which extends from z_arp=0.25045 to z_node=0.291 in the redshift delta of z_Δ=z_node-z_arp=0.04054.
D'_Q3C273 = (H_Q3C273/58.04)D_Q3C273 = 3.0846x10⁹ ly or 946.49 Mpc, which now would calculate an increase in the Hubble Constant as H_Q3C273 = (58.04)D'_Q3C273 /D_Q3C273 = 77.40 km/Mpc.s indicating the reason for the various inconsistent measurements for the Hubble Constant, when applied in the Local Flow.
The ESA-NASA measurements from the Hubble Space telescope and measuring Cepheid variable stars in the nearby Magellanic Clouds, have obtained a much larger Hubble Constant of 74.03 Hubble units, than the Planck Mission's 67.8 Hubble units.

http://sci.esa.int/hubble/61318-lat...onstant-calculations-is-not-a-fluke-heic1908/


As shown, the Redshift-Correction-Correlation for a given redshift and the linearity of the Hubble Law in the Local Flow requires an adjustment of the applied Hubble parameter calibrated and relative to the fixed nodal Hubble Constant H_o=c/R_Hubble.
As the Local Flow is characterized by the Critical Redshift z_{nodalintersection}=z_ni=0.10943 of the nodal intersection in the mirrored negative spacetime from the positive spacetime of the Earth-Time Observer; the corrected redshift values for the Local Flow from z_ni to z_node are imaged at the nodal coordinate for z_node=0.291, which is n_p-1=0.1327117 n-units or ... = 2.120x10²⁵ m* from the position of the Cosmic Wave Surfer.

The nodal mirror of the Inflaton defines a redshift displacement of 2.24 Billion ly from the present observer for multiple redshift values for ylemic or neutron star objects and incorporating Quasars, Blazars and AGNs within the Local Flow. Quasar Q3C273 so is an ylemic object imaged in the Local Flow and positioned relative to the nodal redshift boundary.

The Markarian (UV-emission characteristic) galaxy M231 has a measured redshift of z_M231=0.04147=v'/c and is near z_Δ=z_node-z_arp=0.04054 for D=zc/H.
This redshift so is in the Local Flow and must be corrected by n_M231=√{c/v} - 1 = 4.9106 - 1 = 3.9106 and for a n-cycle time coordinate exceeding that of the boundary value of n_present = 1.1327117... in the third Hubble semi-cycle 4-3.9106=0.08942 n-units from the node n=4-n_ps as f_ps as a projected electromagnetic age for the universe of n_future=65.9953 Gy from n_past=0.08942 as 1.5090 Gy.

Applying the Alpha-Redshift equation z_red(z_m) = 0.37045(z_m) + 0.25045 gives a 'local flow correction' of: (z(0.04147)=0.26581), for which {v'/c=(z²+2z)/(z²+2z+2)=0.23144} = {1/(n'+1)²} for a corrected n'=√(1/0.23144) - 1 = 1.07864 positioning the corrected redshift into the second Hubble semi-cycle for a applicable n-cycle coordinate of n_p-1.07864=0.05407 n-units from n_p.
This position is D'_M231 = 8.638903x10²⁴ m* or 0.91252 Gy from the present observer.
D_M231 = 0.04147c/(66.92 [km/Mpc.s]*) = 0.04147c/{66.92/(3.0857x10¹⁹)} = 5.7366x10²⁴ m*= 605.95x10⁶ ly = 185.87 Mpc

H_M231 = (58.04)D'_M231 /D_M231 = 87.40 km/Mpc, indicating the linear increase in the Hubble parameter under utility of the Hubble Law in the Local Flow. Markarian galaxy M231 can so be used as observational evidence for the redshift limit applying the Hubble Law for the low redshift cosmology in z_Δ=z_node-z_arp=0.04054 for D=zc/H.

The limiting Hubble parameter for this bound then becomes Dz_Δ = 0.04054c/(66.92 [km/Mpc.s]*) = 0.04054c/{66.92/(3.0857x10¹⁹)} = 5.6079x10²⁴ m*= 592.36x10⁶ ly = 181.76 Mpc for Hz_Δ = (58.04)D'z_Δ /Dz_Δ = 87.52 km/Mpc.s, with n(D'z_Δ)=n_p-1.0798=0.05293 from z(0.04054)=0.26547 and v'/c=0.23118 and n'=1.0798 for D'z_Δ = 0.05293R_Hubble = 8.4564x10²⁴ m* = 0.89324 Gy from the present observer.

As z_M231=0.04147 is smaller than z_ni=0.10943, Markarian 231, as all similar redshift-luminosity measurements is not imaged in the nodal boundary. The z_arp redshift is the maximum variation for the present epoch in the Hubble-Oscillation and the fluctuation of the Hubble parameter as the cosmic frequency is mirrored about H'_o(n_p)=H_o/(2-n_p), valid for the (n=1 to 2)-cycle; hence H'_o(n_p)= 58.04/0.8673=66.92 Hubble units.
At the even nodes, say at (n_p=2), (H'_o) quantizes as (f_ps) in the pixilation of spacetime.

At the odd nodal images however, (H'_o) would assume its nodal value of 58.04 Hubble Units.

The Hubble 'Constant' subsequently varies with redshift at any cycle time (n); increasing from 58.04 to 66.9 in the z-intervals (0.10943-0.25045) and (0.2910-0.3432) and decreasing from 66.92 to 58.04 in the z-intervals (0.25045-0.2910) and (1.080-1.840) for the present Hubble epoch.

The 'arpian redshift' as variation maximum is situated at n-coordinate 0.8673, implying that correctly interpreted spectroscopic measurements must converge at a Hubble-Constant of 66.9 Hubble units and a projected mapped age for the universe of (0.8673x16.88 billion years) or 14.64 billion years. For z=(0.3431-1.082), (H_o'=66.9) and the nodal intervals z=(0-0.110) and (z from 1.840) set it as (58.04).

This is a simple yet profound solution to the 70-year search to finetune the 'Hubble-Constant'.
The disagreement regarding the measurements of the Hubble parameter is resolved in the reflection of EMR parameters. All astronomical and cosmological measurements engage optical instruments to catch photons and all of astrochemistry and astrophysics depends on spectrum analysis. So the universe is 'well behaved' after all and decelerating under its own gravity, modified in the quintessence.


Then the 25%, on average, discrepancy in the luminosity of the examined supernovae applies the old 'Hubble Law' in the proportionality of the nodal Hubble-Event-Horizon R_H to an object receding with velocity v'=H'_oxR_H as an epoch dependent 'Hubble Constant' and as the linear proportionality constant between recessional velocity and the distance to the object.

In the case of the quasar 'Q3C273', the measured redshift (z=0.1583) relates a recessional velocity of v'=0.1583c; which is then 'corrected' to calculate the n-cycle position of 'Q3C273', allowing a Hubble-independent determination of its distance from the observer.

The distance to 'Q3C273' differs in for H'=67.8 (Planck Mission) for 2.28 Billion ly and H'= 74.0 (ESA-NASA) for 2.09 Billion ly and H'= 66.92 (Redshift corrected) for 3.08 Billion ly.
The difference between H'=67.8 and H'=66.9 in terms of the distance measurements so is (3.08-2.28)/3.08 = 0.260 or 26% to reflect the 'dimming' effect for the measured luminosities.

The spectroscopic measurements incorporate a natural 'dimming effect' in luminosities, due to the cosmological objects, which are physically nearer, than their redshift indicate, appearing to be further away also in the electromagnetic universe, than they truly are and so the theoretical predictions of their distances are correct in principle, but require modification via the old Hubble Law, calculating a 'Hubble Constant', whose value oscillates between its constant values at the even and odd nodes as f_ps=c/λ_ps=3x10³⁰ and H_o=c/R_Hubble=1.87773x10^-18 respectively .

​

And at higher redshifts, passing the imaging interval from (z=0.291 to 0.343), the seeming cosmic acceleration intensifies until the other imaging interval from (z=1.080 to 1.840) has been reached and centered at z=0.612 as the halfway coordinate between the imaging coordinate intervals for the onset of the Dark Energy-Quintessence and the two self-relative Universal Observers described.

The Cosmic-Wave-Surfer measures the cosmological parameters from its present and measures the universal past in time and the Big Bang Observer measures those parameters from its present in an universal future. The apparent cosmic acceleration hence becomes an imaged double boundary-nodal-mirror effect.
The Alpha-Variation measures shifts in wavelength, which have passed through the described intervals and a 'dip' in the constant is derived from the mathematical analysis. The magnitude of that dip is calculated as about 80 parts per million and is a result of changing the measured value for the charge quantum e in Alpha = 2πke²/hc = e²/2ε_ohc = 60πe²/h.

The Alpha-Variation is the dimensional intersection of M-C-space, 10D-C-space forming a holographic image in 12D-F-space. The charge quantum (e) is defined via the Riemann Analysis of B(n), the supersymmetric wavefunction of the universe:
The Universal Wavefunction B(n) = [2e/hA]exp(-AlphaxT(n)) with units of 'Inverse Energy' redefined in the multidimensional context of string-membrane unification physics as units of magneto charge C* and unit-dimensionally equivalent to the Gravitational Parameter [GM]=[N.m².kg/kg²]=[m³/s²]=[C*] as a unit for physicalized 'Source Energy' Consciousness, descriptive as a quantum angular acceleration (or quantum spin) acting upon a spacetime volumar from a constant boundary-initial condition for df/dt maximized in {df/dt}|_max=f_ps² as 9x10⁶⁰ frequency-vibration eigenstates.

For the Universal Wavefunction {T(n) =...- 3 - 2 - 1 +0+ 1 + 2 + 3 +...= n(n+1)} and the Feynman-Path-Integral for all particle histories as an alternative formulation to the Schrödinger- Dirac- and Klein-Gordon Equations for the quantum mechanistic probability distribution of quantum states in the particle-wave duality.

The Action Law of (Action=ee*) manifests the lightspeed (c)-independent form of Alpha and can then be calibrated via the definition of the (c)-inclusive form in magnetic constant (μ_o). {Alpha = 60πe²/h = e²/(2ε_ohc) = μ_oce²/(2h) = 1/137.0470731}
A Newton-Raphson iteration for B(n) and the boundary condition {T(n)=i² in B{-[1/2]+-i(½√3)}, with a first approximation: (e₁=(½hA=1.618221145x10-¹⁹ C*) converges to: (e=1.606456344x10^-19 C*).

Abstract time in F-Space is defined as: N=Minimum Radius/Maximum Radius = λ_ps/R_Hubble =λ_ps/R_max = n_ps and so allows the definition of Inverse Time as frequency parameter physicalizing this abstraction for time in modular mirror duality made manifest in the string epoch of the Inflaton.

This then defines the GENESIS BOSON as the Particle of creation using the fundamental constants of Creation from the SE_ps algorithms. Those constants are then used inductively in the future by any sufficiently mentally evolved and cosmically self-aware civilization to construct self-consistent and logical measurement systems to rediscover their own nature and origins in a self-induction of physical consciousness of their own cocreated Genesis in a perceived time arrow of entropy, flowing apparently from the past to the present to the future.

In practical terms, this engages the measurement and analysis of two fundamental constants, namely the speed of light 'c' and the Planckian quantum constant 'h' to relate the quantum as a micro energy self-state (eigenvalue) to what is termed the classical physics of macro self-states exemplified in the theoretical physics of Newton, Maxwell and Einstein in scientific models of reality and encompassing mechanics, electromagnetism and the relativities respectively.
The dimensional analysis of 'hc' as a energyxdisplacement parameter suffices to calibrate the unitary mensuration parameters for mass, displacement and time, say in the Earth-Terran System International or SI-system of measurements of fundamental quantities, say here the kilogram, the meter and the second respectively.

The other elementary units in the SI-system are derived from the algorithmic master-constant set and comprise the Kelvin for temperature as kinetic measure of the quantum states, the Ampere and Coulomb for electric current, the mole for molarity , the candela for luminosity with the ster-radian an additional geometrized unit for angular measures.

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



Dimensional Unit Calibration:

[m/s]/[m*/s*] = [c*/c] = [3x10⁸/2.99792458x10⁸] = [1.000692286] for {m/m*} = {1.000692286} {s/s*}
[Js]/[J*s*] = [h*/h] = [6.66666666..x10^-34/6.62607004x10^-34] = [1.006126803] for {J/J*} = {1.006126803} {s*/s}
[m⁵/s³]/[m⁵/s³]* = {[m/m*]²}.[c*/c]³ = G_o*h*/G_oh = 30ch*/30c*h = [c/c*][h*/h] = [0.999308193x1.00612803] = [1.005431984]
for {m/m*} = [c/c*]².√[h*/h] = [0.998616864x1.00305872] = [1.001671357]
for {m}² = 1.00334349 {m*}² and m = 1.001671357 m* and m* = 0.998331431 m
s = {m/m*}.[0.999308193] s* = [1.001671357x0.999308193] s* = 1.000978394 s* and {m/s} = 1.000692286 {m/s}* for {m/s}² = 1.00138505 {m*/s*}² as c²
J = {s*/s}[h*/h] J * = [0.999022562x1.006126803] J* = 1.005143377 J* and J* = 0.994882942 J
kg = {s*/s}.{s/m}².{m*/s*}².[h*/h] kg* = {s/s*}{m*/m}².[h*/h] kg* = [1.000978394x0.996665646x1.006126803] kg* = 1.003753126 kg*
[H/m]/[H*/m*] = [J/J*][m*/m][C*/C]².[s/s*]² = μ_o*/μ_o = [120π/c*]/[4πx10^-7]for C = √{[Js/J*s*][m*s/ms*]} C* =√{[h*/h][c/c*]} C* = √[1.006126803/1.000692286] C* = 1.002711702 C*
[eV]/[eV*] = [e^±J]/[e^±J]* = [e^±/e^±*].[J/J*] for eV = [1.60217662x10^-19/1.606456344x10^-19].[1.005143377] eV* = 1.00246560 eV*
[J/K]/[J*/K*] = {J/J*}.{K*/K} = [k*/k] = [1.411721579x10^-23/1.380649x10^-23] = [1.022505777] for K = [J/J*]/[1.022505777] K* = [1.005143377/1.022505777] K*= 0.983020397 K*

(m*= 0.998331431 m; s*= 0.999022562 s ; kg*=0.99626091 kg) in calibration of the base master constants (h/h*, c/c*, [G_o]u=(1/30c)) and we note the numerical constancy for the magnetic constant in both mensuration systems: (μ_o)=4πx10^-7 Henry/m (H/m) in (SI) and (μ_o)=120π/c (H*/m*) in (*).
We recall that: (c=2.99792458x10⁸ m/s (SI) and c*=3x10⁸ m*/s* (*)).

The cosmic or universal value of alpha so remains constant in all cosmological time frames; with the fluctuation found to depend on an asymptotically constant strong interaction constant as a function of alpha.
In the SI measurement system Planck's constant h = 6.62607004x10^-34 Js and the speed of light is c = 2.99792458x10^-8 m/s and the electron charge are e=1.60217662x10^-19 C for a bare electron mass of 9.10938356x10^-31 kg.

In a mensuration system in which c would be precisely 3x10⁸ (m/s)*; the following conversions between the SI-system and the *-system are applied in this paper.

{s}​	=​	1.000978394​	{s*}​	=​	0.999022562​	{s}​
{m}​	=​	1.001671357​	{m*}​	=​	0.998331431​	{m}​
{kg}​	=​	1.003753126​	{kg*]​	=​	0.996260907​	{kg}​
{C}​	=​	1.002711702​	{C*}​	=​	0.997295631​	{C}​
{J}​	=​	1.005143377​	{J*}​	=​	0.994882942​	{J}​
{eV}​	=​	1.00246560​	{eV*}​	=​	0.997540464​	{eV}​
{K}​		0.98301975​	{K*}​	=​	1.017273559​	{K}​

Furthermore, there exists one fundamental constant in the magnetic permeability constant μo = 4πx10^-7 H/m which becomes numerically equal in the Maxwell constant μ_o = 1/ε_oc² in an applied fine structure μ_o.ε_o = {120π/c}.{1/120πc} = 1/c² (s/m)²; (s/m)²*. Subsequently in the calculation of alpha, the speed conversion must be incorporated for unitary consistency.

Alpha remains constant for a cosmology descriptive of a non-accelerating cosmology; but will result in a change in the electric charge quantum in a cosmology, which measures an accelerated spacial expansion, which can however be the result of a self-intersection of the light path for particular cosmological redshift intervals in an oscillating cosmology.
https://cosmosdawn.net/index.php/en...-alpha-variation-and-an-accelerating-universe

Here a particular alpha variation reduces the SI-measurement for the square of the charge quantum e in a factor of (1.6021119x10^-19/1.60217662x10^-19)² = 0.99991921...for a calibrated:

alpha variation α_var = 1 - (1.6021119x10^-19/1.60217662x10^-19)² = 1 - 0.9999192 = 8.08x10^-5.........[Eq.10]

Alpha α = μ_oce²/2h = e²/2ε_ohc
= 2π.(2.99792458)(1.6021119)²x10^-37/(6.62607004x10^-34) = 60πe²/h = 7.2967696x10^-3 = 1/137.047072

The Henry is a derived (SI) unit for magnetic inductance and has base units (Js²/C²=kgm²/C²), which so must give the (C to C*) unitary calibration in (μ_o/μ_o*)=1=0.994598576 C*²/C², which gives (C*=0.997295631C) and defines the (SI)-Coulomb Charge quantum as: (e=0.997295631e*=1.6021119x10^-19 C (SI)).
The textbooks of SI-physics have (e'=1.60217662x10^-19 C (SI)), however and a value which differs from the value demanded by the magnetic constant (μ_o ) in a factor of (e'/e=1.0000403).
As the electropolar charge quantum appears squared in the Alpha-Constant, the Alpha-variation so becomes (1.0000807), with the old value of (e') exceeding the new value of (e) in so 4 parts in 100,000 and [Alpha]' greater in magnitude than Alpha by 81 parts in a million and in agreement with the Churchill-Webb measurements of 1998, increasing from Alpha = μ_oc.e²/2h = 1/137.047075 to Alpha = 1/137.036003.

Measuring Alpha even further back towards the Quantum Big Bang with increasing redshift, would better approximate the 80 parts per million increase in Alpha from say lower deviations at the say 8 parts per million at lower redshifts.
So the Alpha-Dip indicates that the textbook value for the electropole is fractionally too high; but that the Alpha Finestructure-Constant remains indeed constant, once the variation in the electronic charge quantum is taken into account.

Because the magnetic permeability constants are numerically the same in both the (SI) and the (*) unitary measurement systems; but ε_o = 1/120πc = 8.841941283x10^-12 (F/m)* and is ε_o = 8.8541878176x10^-12 F/m (SI), the (SI) measurement is too large by a factor of 1.00138505 to correlate correctly with the magnetic permeability constant μ_o to give the Maxwell constant μ_oxε_o = (120π/c).(1/120πc) = 1/c².

In the attempt to explain the Alpha-Dip, some theorists have proposed a 'slowing down' of (c).
Recent formulations by populist physicist Paul Davies and in co-authorship with Tamara Davis and Charles Lineweaver from the Department of Astrophysics at the University of New South Wales, Sydney, Australia have followed the wrong avenues for the interpretation of the data however.

In a paper published in ('Nature': 'Black Holes constrain varying constants'; August 8th, 2002), the authors propose a varying light speed to be responsible for the Alpha-Dip and discount any possible variation in the electro charge quantum.
Davies' argument that an increase in (e) would alter the evolution of Black Holes in their entropic definitions does not consider that a product of the Boltzmann Constant (defining entropy), with (e) forms a fundamental fine-structured constant in its own right.

​

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

​

​

As E*.e*= E_psx1/E_ps = 1 as fundamental unity in the 11D Membrane-Mirror-Space of modular duality with e* the magneto charge; one can heuristically state that (Energy E x charge quantum e) in the lower dimensional C-Line-Space C can be expressed as the inversed identity in the form of 1/T.
This then sets E.e=kTe=1 for [ek]=1/T and using an inverse proportion for mass in the lower dimensionality: [e*k*] = 1/T* sets a function f(n) = [ek]/[e*k*] = [T*/T].
This is the case for the Mass-Temperature inverse proportionality for the evolution of Black Holes from microstates to macro states and as in the Hawking Mass-Temperature relation for Black Holes:
{Minimum Planck Oscillator = ½hf_Planck = ½m_Planck.c² for T_max=T_ps and T_min=T_ss in string modular T-duality for ½m_Planck.T_Planck = (1/8π)(4π).m_Planck.T_Planck = Hawking Modulus HM = hc³/4πG_ok = M_BHmin.T_BHmax ={c²/4π²}. M_BHmax.T_BHmin.}.​

B(n) is assigned B(n_p) = {[ek](SI)/[ek](*)}, with {[ek](SI)=constant=(1.60217662x10^-19 C)(1.380649x10^-23 J/K) = 2.21204355x10^-42 CJ/K} and using the old (SI) value with the Alpha-Variation for (e'); using (e^±=1.6021119x10^-19 C) without the Alpha-Variation gives {[ek](SI)} = 2.21195419x10^-42 CJ/K}.
The (*)-constant is a relatively fixed constant as: (e^±*k*=2.267869086x10^-42 (CJ/K)*) and subsequently B(n_p) calculates a particular value for n at the asymptote B(n⇒±∞)=0 as:

{[e^±k](SI)/[e^±k]*} = (2.21204355/2.267869086) = 0.975384145 (0.975344742)= [2e/hA].exp(-[Alpha]x[n_p²+n_p]), which yields an unique (n_p) as a complex solution to the quadratic equation by ln(0.975384145/0.992729803) = {ln(0.982527312)/-Alpha} = 2.415747501 = n_p²+n_p for: n_p² + n_p - 2.415747501 = 0 solving as: (n_p=FRB(-½) ± 1.6327117).

For the unfrozen M-space with Alpha-Variation: {10D-root: n_p = 1.1327117 (real) & 12D-root: n_p = -2.1327117 (imaginary)}.
For the unfrozen M-space without Alpha-Variation: {10D-root: n_p = 1.1344063 (real) & 12D-root: n_p = -2.1344063 (imaginary)}.

This 'unfreezing' of M-space then allows the singularity algorithm of the cosmogenesis to manifest in what might be called the sex chromosomes of the universal DNA-encoding in terms of frequency or a number count.
A new physical quantity in 'awareness' is defined as the time differential of frequency and allows the concept of 'consciousness' to be born from the defining qualities of magneto charges.
Electromagneto-monopolar 'Life' derives as consequence of self-inductions of quantum geometric entities, specified from super membranes, macro-crystallized in electropolar self-capacitances and magnetopolar self-inductances, subsequently becoming subject to mutual cross inductances.

The purpose of the superbranial self-replication on ever increasing scales, and until modular duality is reached in minmax boundary conditions; is to establish the multiversal nesting of the smallest within the largest - a process which constituted the beginnings of it all in the 'naked singularity' becoming defined as the Genesis BOSON.


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

Particularly then: ENERGY=hR_max/λ_ps with MASS=hR_max/λ_psc²=0.01183463299 and TEMPERATURE=hR_max/kλ_ps=7.544808988..x10³⁷ and FREQUENCY=R_max/λ_ps=1.59767545..x10⁴⁸

This becomes the 'Atomic-Mass-Unit' in 12D-F-Space in using one protonucleon m_c=Alpha⁹L_planck for every one of the 12 monopolar current loops in the Unified Field of Quantum Relativity (UFoQR).
A first E_ps-Coefficient in the Expansion Series of the fundamental principles from the SE_ps algorithm then crystallizes the 'Counter for matter' in Avogadro's Constant for Molarity:
MASS(20/33)/12m_c = N_avogadro = 6.02242143x10²³ 1/mol*
N=n_ps=λ_ps/R_max in REAL Time relative to the Quantum Big Bang to be created following the string epoch and relating to IMAGINARY TIME relative to this selfsame creation in the Cosmogony of the Genesis Boson of the Abba-Baab 11-dimensional supermembrane. This UNREAL Quantum Relative Time then is the Hubble-FREQUENCY H_o=c/R_max in proportionality to the Source Frequency of the E_ps-Gauge Photon f_ps=c/λ_ps in the expression H_oR_max=c=λ_ps.f_ps

N then becomes the Null time for the initialization of the string/supermembrane-serpent modular duality in the De Broglie phase speed initialization, beginning with the Oscillation (or Bounce) of the Planck-Length and specifies the Instantaneity of Now-Cycle-Time n_ps=H_ot_ps=H_o/t_ss as the Time Instanton t_ps=1/f_ps=f_ss and the Inflaton R_max=R_Hubble=c/H_o with de Broglie Phase speed V_debroglie=R_max.f_ps=R_max.c/λ_ps=c/n_ps as the 'Heartbeat of the Cosmic Mother Black Hole' frequency of the oscillating cosmos in the Cosmology of QR and in the imaginary F-Space Time of NH_o generalised in the Real Time n=H_ot for any time in the evolving Cosmology and minimized in n_ps=H_ot_ps.

(PDF) The Accelerating Universe, Dark Energy & the Alpha Variation | Anthony P Bermanseder - Academia.edu​