Fermi-Dirac corrections to relic abundances

Abstract

We derive an equation for the evolution of the number density of a massive particle species in the early Universe, which correctly accounts for the Fermi-Dirac (FD) statistics. The FD-corrections are sizable and potentially important if the decoupling from the thermal equilibrium takes place at temperatures of the order of, or less than the mass of the particle. This is the case e.g.\ for a few MeV tau neutrino with the ordinary weak interactions.