= Critical-density mass of a thermal relic neutrino
{title2=$m_\nu=\frac{11\pi}{16\zeta(3)}H_0^2M_P^2/T_{\gamma0}^3$}
A standard thermal <Cosmic neutrino background> with one populated <neutrino> and one <antineutrino> helicity per species has $n_\nu+n_{\bar\nu}=3n_\gamma/11$ after <electron-positron annihilation in cosmology>. If this species is nonrelativistic today and dominates a spatially flat matter universe, equate $m_\nu(n_\nu+n_{\bar\nu})$ to the <critical density> $3H_0^2M_P^2/(8\pi)$, using the unreduced <Planck mass>. The <photon number density> gives the displayed conditional mass. Extra populated states or several massive species change the abundance count; vacuum-dominated cosmology changes the density available for matter.
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