 Photon-to-baryon ratio from density parameters

With $n_{\gamma }=0.24Q^3$, $u_{\gamma }=0.66\hslash c{Q}^4$, $Q=k_{B}T/(\hslash c)$ and $n_B={\Omega }_B{\rho }_c/m_p$, eliminate $Q$ using $u_{\gamma }={\Omega }_{\gamma }{\rho }_c{c}^2$. The prefactor is $0.24/0.66^{3/4}=0.328$. Here ${\rho }_c$ is the mass-equivalent cosmological critical density; inserting an energy-density critical value without its $c^2$ conversion would give incorrect dimensions. A numerical estimate needs photon and baryon density parameters as additional inputs.