ρc := 3 c^2/(8 Pi Gn) Ho^2
Gn := 6.67 10^-11 m^3/(kg s^2)
Ho := 100 h km/s/Mpc 
h := 0.72
c := 2.99792 10^8 m/s
Mpc := 3.08568 10^22 m
km := 10^3 m
hbar := 1.05457 10^-34 m^2 kg/s
J := kg m^2/s^2
conv :=  hbar c

ρr :=( Pi^2/30 2 Tg^4 + 3.046 7 Pi^2/120 Tn^4 ) /conv^3

Tn := (4/11)^(1/3) Tg

Tg := 2.726 K   (1.3806503 10^-23 kg m^2 /s^2 /K  )

Tg

ρr

ρc

ρr/ρc

OmegaR0 := 0.00008071281149928993`
OmegaM0 := 0.28

f[z_] := Sqrt[OmegaM0 (1+z)^3 + OmegaR0 (1+z)^4 + (1-OmegaM0 - OmegaR0)]

Ho^-1 NIntegrate[1/f[z]/(1+z),{z,0,Infinity}]

365.25 24 60 60 s/yr

%%/%

OmegaR0 := 0.00008 
OmegaM0 := 0.28

f[z_] := Sqrt[OmegaM0 (1+z)^3 + OmegaR0 (1+z)^4 + (1-OmegaM0 - OmegaR0)]

Ho^-1 NIntegrate[1/f[z]/(1+z),{z,0,Infinity}]

365.25 24 60 60 s/yr

%%/%

13.34 GYRS

OmegaR0 := 0.00008 
OmegaM0 := 0.28

f[z_] := Sqrt[OmegaM0 (1+z)^3 + OmegaR0 (1+z)^4 + (1-OmegaM0 - OmegaR0)]

Ho^-1 NIntegrate[1/f[z]/(1+z),{z,1089,Infinity}]

365.25 24 60 60 s/yr

%%/%

7-YR WMAP ML PARAMETERS

h := 0.703

ρr/ρc

OmegaR0 := 0.0000846636169742597`

OmegaM0 := (0.1116 + 0.02227)/h^2

OmegaM0

Ho^-1 NIntegrate[1/f[z]/(1+z),{z,0,Infinity}]

365.25 24 60 60 s/yr

%%/%

13.79 Gyrs

Ho^-1 NIntegrate[1/f[z]/(1+z),{z,1089,Infinity}]

365.25 24 60 60 s/yr

%%/%

380,000 yrs