Relic-neutrino energy density

For one relic-neutrino species with two internal states, physical momentum $p$, comoving temperature $T_{\nu }$, and mass $m_{\nu }$,It approaches $7{\pi }^2(T_{\nu }/a{)}^4/120$ while relativistic and $n_{\nu }{m}_{\nu }$ after becoming nonrelativistic.

Expanding the relic-neutrino energy density at $T_{\nu }/a\ll m_{\nu }$ givesThe thermal speed decreases as $a^{-1}$ after the neutrinos become nonrelativistic.