Blue Flower

 

Yn = RHubble/rWeyl = 2pRHubble/lWeyl = wWeyl/Ho = 2pnWeyl = nps/2p = 1.003849x1049


2nd Inflaton/Quantum Big Bang redefines

for k=1: RHubble(1) = n1RHubble = c/Ho(1) = (234.472)RHubble = 3.746x1028 m* in 3.957 Trillion Years for critical nk 3rd Inflaton/Quantum Big Bang redefines

for k=2: RHubble(2) = n1n2RHubble = c/Ho(2) = (234.472)(245.813)RHubble = 9.208x1030 m* in 972.63 Trillion Years for critical nk 4th Inflaton/Quantum Big Bang redefines

for k=3: RHubble(3) = n1n2n3RHubble = c/Ho(3) = (57,636.27)(257.252)RHubble = 2.369x1033 m* in 250.24 Quadrillion Years for critical nk 5th Inflaton/Quantum Big Bang redefines

for k=4: RHubble(4) = n1n2n3n4RHubble = c/Ho(4) = (14,827,044.63)(268.785)RHubble = 6.367x1035 m* in 67.26 Quintillion Years for critical nk ... (k+1)th Inflaton/Quantum Big Bang redefines

for k=k: RHubble(k) = RHubble P nk = c/Ho P nk .....
nk = ln{wWeylRHubble(k)/c}/lnY = ln{wWeyl/Ho(k)}/lnY

 

A general dark energy equation for the kth universe (k=0,1,2,3,...) in terms of the parametrized Milgröm acceleration A(n); comoving recession speed V(n) and scalefactored curvature radius R(n):


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


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


and where


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


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


for Instanton-Inflaton Baryon Seed Constant Wo = Mo*/MH* = 0.02803 for the kth universal matter evolution k=0

for Reset n=nps=Hot and Lo/adeBroglie = GoMo(nps+1)2/{RH3nps2(fps2)} = GoMo/RHc2 = Mo/2MH = ½Wo k=1

for Reset n=1+nps and Lo/adeBroglie = GoMo(1+nps-1+n1)2/{[n1]2.RH3(1+nps-1)2(n1fps2)} = Mo/2n1MH = Mo/2MH* = ½Wo* k=2

for Reset n=n1+1+nps and Lo/adeBroglie = GoMo(n1+1+nps-1-n1+n1n2)2/{[n1n2]2.RH3(n1+1+nps-1-n1)2(n1n2fps2)} = ½Wo** k=3

for Reset n=n1n2+n1+1+nps and Lo/adeBroglie = GoMo(n1n2+n1+1+nps-1-n1-n1n2+n1n2n3)2/{[n1n2n3]2.RH3(n1n2+n1+1+nps-1-n1-n1n2)2(n1n2n3fps2)} = ½Wo*** ......


with nps = 2pPnk-1.Xnk = lps/RH = Hotps = Ho/fps = ctps/RHand RH=2GoMH/c2


No=Hoto/no=Hot=n N1=Hot1/n1=(n-1)/n1 N2=Hot2/n1n2=(n-1-n1)/n1n2 N3=Hot3/n1n2n3=(n-1-n1-n1n2)/n1n2n3
Nk=Hotk/Pnk = {n-SPnk-1}/{Pnk}


...... dn/dt=Ho .....


with nps = 2pPnk-1.Xnk = lps/RH = Hotps = Ho/fps = ctps/RH and RH=2GoMH/c2
.....
Nk=Hotk/Pnk =(n-SPnk-1)/Pnk tk = t - (1/Ho)SPnk-1 = NkPnk/Ho = (n-SPnk-1)/Ho for no=1 and No=n


to=t=n/Ho=No/Ho=nRH/c t1=t-1/Ho=(n-1)/Ho=[n1N1]/Ho t2=t-(1+n1)/Ho=(n-1-n1)/Ho=(n1n2N2)/Ho t3=t-(1+n1+n1n2)/Ho=(n-1-n1-n1n2)/Ho=(n1n2n3N3)/Ho .......


R(n)=R(No)=1.RH{n/[n+1]}=1.RH{n/[n+1]} R1(N1)=1.n1RH{N1/[N1+1]}=1.n1RH{[n-1]/[n-1+n1]} R2(N2)=1.n1n2RH{N2/[N2+1]}=1.n1n2RH{[n-1-n1]/[n-1-n1+n1n2]} R3(N3)=1.n1n2n3RH{N3/[N3+1]}=1.n1n2n3RH{[n-1-n1-n1n2]/[n-1-n1-n1n2+n1n2n3]} .......


Rk(Nk)=Pnk.RH{(n-SPk-1)/(n-SPk-1+Pnk}
Rk(n)|dS = PnkRH(n-SPnk-1)/{n-SPnk-1+Pnk}
.....= RH(n/[n+1]) = n1RH(N1/[N1+1]) = n1n2RH(N2/[N2+1]) =.....


Rk(n)|AdS = RH(n-SPnk-1)
.....= RH(n) = RH(N1)=RH(n-1) = RH(N2)=RH(n-1-n1) =.....


Vk(n) = dRk(n)/dt = c{Pnk}2/{n-SPnk-1+Pnk}2
.....= c/[n+1]2 = c/[N1+1]2=c(n1)2/[n-1+n1]2 = c/[N2+1]2 =c(n1n2)2/[n-1-n1+n12n22]2 =.....


Vk(n) = dRk(n)/dt = RH.Ho = c in AdS
.....= c = c = c =.....


Ak(n) = d2Rk(n)/dt2 = -2cHo(Pnk)2/(n-SPnk-1+Pnk)3
.....= -2cHo/(n+1)3 = -2cHo/n1(N1+1)3=-2cHo{n1}2/[n-1+n1]3 = -2cHo/n1n2(N2+1)3=-2cHo(n1n2)2/[n-1-n1+n1n2]3 =.....


Ak(n) = d2Rk(n)/dt2 = 0 in AdS

 

 

Scalefactors:


ak(n) = Nk/[Nk+1] = {n-SPnk-1}/Pnk}/{(n-SPnk-1+Pnk)/Pnk} = {n-SPnk-1}/{n-SPnk-1+Pnk}
....= (n)/(n+1) = (n-1)/(n-1+n1) = (n-1-n1)/(n-1-n1+n1n2) =......


GoMo is the Gravitational Parameter for the Baryon mass seed; Curvature Radius RH = c/Ho in the nodal Hubble parameter Ho and c is the speed of light

Friedmann's acceleration equation and its form for the Hubble time derivative from the Hubble expansion equation substitutes a curvature k=1 and a potential cosmological constant term; absorbing the curvature term and the cosmological constant term, which can however be set to zero if the resulting formulation incorporates a natural pressure term applicable to all times in the evolvement of the cosmology.


Deriving the Instanton of the 4D-dS Einstein cosmology for the Quantum Big Bang (QBB) from the initial-boundary conditions of the de Broglie matterwave hyper expansion of the Inflaton in 11D AdS then enables a cosmic evolution for those boundary parameters in cycle time n=Hot for a nodal 'Hubble Constant' Ho=dn/dt as a function for a time dependent expansion parameter H(n)=Ho/T(n)=Ho/T(Hot).


It is found, that the Dark Matter (DM) component of the universe evolves as a function of a density parameter for the coupling between the inflaton of AdS and the instanton of dS space times. It then is the coupling strength between the inflationary AdS brane epoch and the QBB dS boundary condition, which determines the time evolution of the Dark Energy (DE). Parametrization of the expansion parameter H(n) then allows the cosmological constant term in the Friedmann equation to be merged with the scalar curvature term to effectively set an intrinsic density parameter at time instantenuity equal to L(n) for Lps=LQBB=GoMo/lps2 and where the wavelength of the de Broglie matter wave of the inflaton lps decouples as the Quantum Field Energy of the Planck Boson String in AdS and manifests as the measured mass density of the universe in the flatness of 4D Minkowski spacetime.


dH/dt + 4pGr = - 4pGP/c2
... (for V4/10D=[4p/3]RH3 and V5/11D=2p2RH3 in factor 3p/2)


For Hypersphere Volumar of 3-sphere: d2{V4}/dR2 = d2p2R4}/dR2 = d{2p2R3}/dR = 6p2R2 Surface Area of Horn Torus (2pR)(2pR)= 4p2R2
Linearisation of lps = 2prps = npsRH = c/fps = HoRH/fps


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

 

areset = Rk(n)AdS/Rk(n)dS + ½ = n-SPnk-1+Pnk +½ Scalefactor modulation at Nk = {n-SPnk-1} = ½ reset coordinate


{dH/dt} = areset .d{Ho/T(n)}/dt = - Ho2(2n+1)(n+3/2)/T(n)2 for k=0


dH/dt + 4pGr = - 4pGP/c2


-Ho2(2n+1)(n+3/2)/T(n)2 + GoMo/{RH3(n/[n+1])3}{4p} = L(n)/{RH(n/[n+1])} + L/3 -2Ho2{[n+1]2-¼}/T[n]2 + GoMo/RH3(n/[n+1])3{4p} = L(n)/RH(n/[n+1]) + L/3 -2Ho2{[n+1]2-¼}/T(n)2 + 4p.GoMo/RH3(n/[n+1])3 = L(n)/RH(n/[n+1]) + L/3


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

L(n)/RH(n/[n+1]) = - 4pGP/c2 = GoMo/RH3(n/[n+1])3 -2Ho2/(n[n+1]2)
and L = 0 for -P(n) = L(n)c2[n+1]/4pGonRH =L(n)Hoc[n+1]/4pGon = Moc2[n+1]3/4pn3RH3 - Ho2c2/2pGon[n+1]2

For n=1.13242:............ - (+6.7003x10-11 J/m3)* = (2.12682x10-11 J/m3)* + (-8.82709x10-11 J/m3)* Negative Dark Energy Pressure = Positive Matter Energy + Negative Inherent Milgröm Deceleration(cHo/Go)​
 

The Dark Energy and the 'Cosmological Constant' exhibiting the nature of an intrinsic negative pressure in the cosmology become defined in the overall critical deceleration and density parameters. The pressure term in the Friedmann equations being a quintessence of function n and changing sign from positive to negative to positive as indicated. For a present measured deceleration parameter qdS=-0.5585, the DE Lambda calculates as -6.700x10-11 (N/m2=J/m3)*, albeit as a positive pressure within the negative quintessence.


In the early radiation dominated cosmology; the quintessence was positive and the matter energy dominated the intrinsic Milgröm deceleration from the Instanton n=nps to n=0.18023 (about 3.04 Billion years) when the quintessence vanished and including a Recombination epoch when the hitherto opaque universe became transparent in the formation of the first hydrogen atoms from the quark-lepton plasma transmuted from the X-L Boson string class HO(32) of the Inflaton epoch preceding the Quantum Big Bang aka the Instanton.


From the modular membrane duality for wormhole radius rps = lps/2p, the critical modulated Schwarzschild radius rss = 2plss = 2px1022 m* for lps = 1/lss and for an applied scalefactor a = n/[n+1] = lss/RH = {1-1/[n+1]}


for a n=Hot coordinate nrecombination = 6.259485x10-5 or about 6.259485x10-5(16.88 Gy) = 1.056601 Million years attenuated by exp{-hf/kT} = e-1 = 0.367879 to a characteristic cosmological time coordinate of 0.36788x1.056601 = 388,702 years after the Instanton nps.


The attenuation of the recombination coordinate then gives the cosmic temperature background for this epoch in the coordinate interval for the curvature radius R(n=2.302736x10-5) = 3.67894x1021 m* to R(n=6.259485x10-5) = 1022 m*. This radial displacement scale represents the size of a typical major galaxy in the cosmology; a galactic structure, which became potentialised in the Schwarzschild matter evolution and its manifestation in the ylemic prototypical first generation magnetar-neutron stars, whose emergence was solely dependent on the experienced cosmic temperature background and not on their mass distributions.


The temperature evolution of the Instanton can be written as a function of the luminosity L(n,T) with R(n)=RH(n/[n+1]) as the radius of the luminating surface L(nps,T(nps) = 6π2lps2.σ.Tnps4 = 2.6711043034x1096 Watts*, where σ = Stefan's Constant = 2π5k4/15h3c2 and as a product of the defined 'master constants' k, h, c2, π and 'e'.
L(n,T) = 3HoMo.c2/550n and for Temperature T(nps) ----------- T(nps) = 2.93515511x1036 Kelvin*.


T(n)4 = HoMoc2/(2p2sRH2[550n3/[n+1]2]) for T(n)4 = {[n+1]2/n3}HoMoc2/(2p2sRH2[550]) = 18.1995{[n+1]2/n3} (K4/V)* for a temperature interval in using the recombination epoch coordinates T(n1=6.2302736x10-5) = 2945.42 K* to T(n2=6.259485x10-5) = 2935.11 K*

 

 

Hubble Parameters:


H(n)|dS = {Vk(n)}/{Rk(n)} = {c[Pnk]2/[n-SPnk-1+Pnk]2}/{Pnk.RH[n-SPnk-1]/(n-SPnk-1+Pnk)} = PnkHo/[n-SPnk-1][n-SPnk-1+Pnk]
H(n)|dS = PnkHo/{[n-SPnk-1][n-SPnk-1+Pnk]}


.....= Ho/{[n][n+1]}=Ho/T(n) = n1Ho/{[n-1][n-1+n1]} = n1n2Ho/{[n-1-n1][n-1-n1+n1n2]} =..... for dS


H(n)'|dS = Ho/[n-SPnk-1] for oscillating H'(n) parameter between nodes k and k+1 ||nps+SPnk-1 - SPnk||
H(n)|AdS = H(n)'|AdS = {Vk(n)}/{Rk(n)} = c/{RH(n-SPnk-1}
H(n)|AdS = H(n)' = Ho/(n-SPnk-1)


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


For initializing scale modulation Rk(n)Ads/Rk(n)dS + ½ = PnkRH(n-SPnk-1)/{PnkRH(n-SPnk-1)/(n-SPnk-1+Pnk)} + ½Pnk = {n - SPnk-1 + Pnk + ½} reset coordinate
dH/dt = (dH/dn)(dn/dt) = -Pnk.Ho2{(2n-2SPnk-1+Pnk)(n-SPnk-1+PnkPnk)}/{n2-2nSPnk-1+(SPnk-1)2+Pnk[n-SPnk]}2 = -2PnkHo2{[n - PSnk-1 + Pnk]2 - ¼SPnk2}/{(n-SPnk-1)(n-SPnk-1+Pnk)}2


dH/dt|dS = -2PnkHo2{[n - PSnk-1 + Pnk]2 - ¼(SPnk)2}/{(n-SPnk-1)(n-SPnk-1+Pnk)}2


.....= -2Ho2([n+1]2-¼)/{n[n+1]}2 = -2n1Ho2{[n-1+n1]2-¼n12}/{[n-1][n-1+n1]}2 = -2n1n2Ho2{[n-1-n1+n1n2]2-¼n12n22}/{[n-1-n1][n-1-n1+n1n2]}2 =.....

dH/dt = (dH/dn)(dn/dt) = -Hoc/{(RH(n-SPnk-1)2} = -Ho2/{n-SPnk-1}2 for AdS


dH/dt|AdS = -Ho2/{n-SPnk-1}2


.....= -Ho2/n2 = Ho2/(n-1)2 = -Ho2/(n-1-n1)2 = .....

dH/dt + 4pGor = - 4pGoP/c2


dH/dt + 4pGoMo/Rk(n)3 = Lk(n)/Rk(n) = - 4pGoP/c2 = GoMo/Rk(n)3 - 2(Pnk)Ho2/{(n-SPnk-1)(n-SPnk-1+Pnk)2 } for dS with
{-4p}P(n)|dS = Moc2/Rk(n)3 - 2Pnk(Hoc)2/{Go(n-SPnk-1)(n-SPnk-1+Pnk)2} = Moc2/{RH(n-SPnk-1)}3 - 2PnkHo2c2/{Go(n-SPnk-1)(n-SPnk-1+Pnk)2}

 

Lk(n)/Rk(n) = -4pGoP/c2 = GoMo/Rk(n)3 - dH/dt = GoMo/{RH(n-SPnk-1)}3 - Ho2/{n-SPnk-1}2 for AdS with
{-4p}P(n)|AdS = Moc2/Rk(n)3 - (Hoc)2/{Go(n-SPnk-1)2} = Moc2/{RH(n-SPnk-1)}3 - Ho2c2/{Go(n-SPnk-1)2}

 

 

Deceleration Parameters:


qAdS(n) = -Ak(n)Rk(n)/Vk(n)2 = -{(-2cHo[Pnk]2)/(n-SPnk-1+Pnk)3}{PnkRH(n-SPnk-1)/(n-SPnk-1+Pnk)}/{[Pnk]2c/(n-SPnk-1+Pnk)}2 = 2(n-SPnk-1)/Pnk


qAdS+dS(n) = 2(n-SPnk-1)/Pnk


qdS(n) = 1/qAdS+dS(n) - 1 = Pnk/{2[n-SPnk-1]} - 1


with Ak(n)=0 for AdS in areset = Rk(n)AdS/Rk(n)dS + ½ = {RH(n-SPnk-1)}/{RH(n-SPnk-1)/(n-SPnk-1+1)} + ½ = n-SPnk-1+1+½


Scalefactor modulation at Nk = {n-SPnk-1}/Pnk = ½ reset coordinate


.....= 2n = 2(n-1)/n1 = 2(n-1-n1)/(n1n2) =..... for AdS .....= 1/{2n} -1 = n1/{2[n-1]} -1 = n1n2/{2(n-1-n1)} -1 =..... for dS

 

 

Temperature:


T(n) =∜{Moc2/(1100sp2.Rk(n)2.tk)} and for tk = (n-SPnk-1)/Ho
Tk(n) = ∜{HoMoc2(n-SPnk-1+Pnk)2/[1100sp2.RH2.(n-SPnk-1)3]}
=∜{Ho3Mo(n-SPnk-1+Pnk)2}/{1100sp2(n-SPnk-1)3} = ∜{18.199(n-SPnk-1+Pnk)2/[(n-SPnk-1)3]}


T(n) .....= ∜{18.2[n+1]2/n3} = ∜{18.2[n-1+n1]2/(n-1)3} = ∜{18.2[n-1-n1+n1n2]2/(n-1-n1)3} =.....

 

 

Comoving Redshift:


z + 1 = √{(1+v/c)/(1-v/c)} = √{([n-SPnk-1+Pnk]2+[Pnk]2)/([n-SPnk-1+Pnk]2-[Pnk]2)} = √{([n-SPnk-1]2+2Pnk(n-SPnk-1)+2(Pnk)2)/([n-SPnk-1]2+2Pnk(n-SPnk-1)} = √{1 + 2(Pnk)2/{(n-SPnk-1)(n-SPnk-1+2Pnk)}
z+1 = √{ 1 + 2/{[n2-2nSPnk-1 +(SPnk-1)2+2n-2SPnk-1} = √{1+2/{n(n+2-2SPnk-1) + SPnk-1(SPnk-1-2)}


....= √{1+2/(n[n+2])} = √{1+2/([n-1][n-1+2n1])} = √{1+2/([n-1-n1][n-1-n1+2n1n2])} =......

 

 

Baryon-Dark Matter Saturation:


WDM = 1-WBM until Saturation for BM-DM and Dark Energy Separation
rBM+DM/rcritical = WoY{[n-SPnk-1]/Pnk}/{(n-SPnk-1)/(n-SPnk-1+Pnk)}3 = MoY{[n-SPnk-1]/Pnk}/{rcriticalRk(n)3}

 

Baryon Matter Fraction WBM = WoY{Nk} = Wo.Y{[n-SPnk-1]/Pnk}

Dark Matter Fraction WDM = WoY{[n-SPnk-1]/Pnk}{1-{(n-SPnk-1)/(n-SPnk-1+Pnk)}3/{(n-SPnk-1)/(n-SPnk-1+Pnk)}3= WoY{[n-SPnk-1]/Pnk}{(n-SPnk-1+Pnk)3-(n-SPnk-1)3}/{n-SPnk-1}3 = WoY{[n-SPnk-1]/Pnk}{(1+Pnk/[n-SPnk-1])3 -1} = WBM{(1+Pnk/[n-SPnk-1])3 -1}

Dark Energy Fraction WDE = 1- WDM - WBM = 1 - WBM{(1+Pnk/[n-SPnk-1])3}

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

WoY{[n-SPnk-1]/Pnk} = rBM+DMRk(n)3/MH = (Nk/[Nk+1]3 = {(n-SPnk-1)/(n-SPnk-1+Pnk)}3 =Rk(n)3/VH = VdS/VAdS for rBM+DM = MH/RH3 = rcritical and for Saturation at 0.035473
(Mo/MH). Y{[n-SPnk-1]/Pnk} = {(n-SPnk-1)/(n-SPnk-1+Pnk)}3 .....= 0.489362=no=n = 115.742=n1N1+1 = 28,440.470=n1n2N2+1+n1 =......at 0.035473

 

 

Baryon-Dark Matter Intersection:
Nk=√2 for n = √2.Pnk + SPnk-1 .....= √2=no=n = 331.593=n1√2 + 1 = 81,745.461=n1n2√2 + 1 + n1 =.....

 

 

Hypermass Evolution:


Yk{(n-SPnk-1)/Pnk} = 2pPnk.RH/lps = Pnk.RH/rps = PnkMH*k/mH*k for MH = c2RH/2Go and mH = c2rps/2Go

 

Hypermass MHyper = mH.Yk{(n-SPnk-1)/Pnk}

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