Abundance of Cosmological Relics in Low-Temperature Scenarios

Abstract

We investigate the relic density n_χof non-relativistic long-lived or stable particles χin cosmological scenarios in which the temperature T is too low for χto achieve full chemical equilibrium. The case with a heavier particle decaying into χis also investigated. We derive approximate solutions for n_χ(T) which accurately reproduce numerical results when full thermal equilibrium is not achieved. If full equilibrium is reached, our ansatz no longer reproduces the correct temperature dependence of the χnumber density. However, it does give the correct final relic density, to an accuracy of about 3% or better, for all cross sections and initial temperatures.