= Cosmic neutrino background
{c}
{wiki}
The <Cosmic neutrino background> is the relic population of <neutrinos> left after <thermal decoupling in cosmology>. As the <universe> expands, their momenta redshift; the decoupled distribution retains a temperature parameter proportional to the inverse <scale factor>, even after massive <neutrinos> become nonrelativistic.
The standard ideal temperature ratio follows from <cosmological entropy conservation>. Assume instantaneous <neutrino decoupling> before <electron-positron annihilation> and negligible <chemical potentials>. The coupled <photon>–<electron>–<Positron> sector initially has entropy degrees of freedom $2+(7/8)4=11/2$, dropping to two after annihilation. Conserving its comoving <entropy> heats the <photons> relative to the freely redshifting <neutrinos>, giving
$$
\frac{T_\nu}{T_\gamma}=\left(\frac4{11}\right)^{1/3}\simeq0.714.
$$
For example, a <photon> <temperature> of $2.725\,\mathrm K$ corresponds to a relic-neutrino temperature parameter near $1.95\,\mathrm K$ in this idealization. Residual interactions during non-instantaneous <neutrino decoupling> slightly modify the distribution, so the simple ratio is an approximation.<Cosmology by David Tong/2 The Hot Universe>[Thermal history, neutrino decoupling and electron-positron entropy transfer]{ref}
Back to article page
