Baryon to photon ratio urgent help

Question

I am having trouble showing that the baryon to photon ratio is

η= n_b/n_γ ~ 2.7x10^-8Ω_bh²

where n_b and n_γ are the number density of baryons and photons respectively, Ω_b is the baryon density parameter Ω_b = ρ_b/ρ_crit, ρ_crit = 1.87x10^-29 h² g cm^-3 and

h = H₀/(100 km s^-1Mpc^-1)

is the dimensionless hubble parameter. Note that the number density of photons in a blackbody background at temperature T is given by

nγ = (k_BT/hc)³ 1/π² ∫₀^∞ (x²dx)/(e^x-1) ~ 0.244(k_BT/hc)³

Take the temperature of the cosmic microwave background as T_CMB = 2.73 K

Answer 1

Lena,

There are many different values suggested for the Hubble constant. If you tell me which one you are using, I may be able to help you.