Baryon to photon ratio In Dodelson's "Modern Cosmology", the current baryon-to-photon ratio is defined as $$ \eta_b \equiv \dfrac{n_b}{n_\gamma} = 5.5 \times 10^{-10} \left(\dfrac{\Omega_b h^2}{0.020}\right). $$
I have tried to found a discussion of the evolution of this parameter, but all I could find was its present value. Why, it seems, is its evolution never mentioned? What approximate value would it have for the early universe?
 A: The baryon number is conserved. Dating from the baryogensis, the baryonic number density is $n_B=N_B/a^3$, where $a$ is the scale factor and $N_B=\text{const}$.
The number of photons isn't strictly conserved. However, it is approximately $10^{10}$ times larger than the number of baryons. Even if photons are sometimes produced in processes involving baryons, it changes the total number of photons only by a tiny fraction. Hence, the photon number density is $n_\gamma=N_\gamma/a^3$ with $N_\gamma\approx\text{conts}$.
Both $n_B$ and $n_\gamma$ contain $a^3$ since we are talking about number density, not energy density (usually denoted by $\rho$). Therefore, their ratio, $\eta$, remains approximately constant.
A: The reference here seems to give a realistic (although brief) description of the calculation you asked about. The answer is: "... for each baryon in the Universe there is 10^10 photons."
A: This ratio goes inversely with the scale factor $a$. The baryon density goes like $a^{-3}$ because of spatial expansion. The photon density has that factor and then an additional $a^{-1}$ because of the Doppler shift, which reduces the energy of each photon.
