 Cosmic neutrino background

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, givingFor 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.^[ref]