Abundance of cosmological relics in low-temperature scenarios

We investigate the relic density nχ of nonrelativistic long-lived or stable particles χ in cosmological scenarios in which the temperature T is too low for χ to achieve full chemical equilibrium. The case with a heavier particle decaying into χ is also investigated. We derive approximate solutions for nχ(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 χ number 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.