Relic-neutrino energy density
= Relic-neutrino energy density
For one relic-neutrino species with two internal states, physical momentum $p$, comoving temperature $T_\nu$, and mass $m_\nu$,
$$
\rho_\nu=\frac1{\pi^2}\int_0^\infty
\frac{p^2\sqrt{p^2+m_\nu^2}}{e^{ap/T_\nu}+1}\,dp.
$$
It approaches $7\pi^2(T_\nu/a)^4/120$ while relativistic and $n_\nu m_\nu$ after becoming nonrelativistic.