 Sudden decay of a dominant nonrelativistic relic

The sudden-decay approximation converts a dominant cold relic's rest-mass density into radiation at $H\simeq \Gamma$, neglecting expansion during the conversion. Its pre-decay radiation temperature obeys $T_{-}^3\simeq 3M_{\mathrm{Pl}}^2{\Gamma }^2/(c_1{g}_{\star }Ym)$, while the reheating temperature is set by the post-decay radiation energy density. Constant relativistic counts and prompt thermalization are additional assumptions.