= Instantaneous photon heating by a decaying relic
{title2=$T_\gamma^+/T_\gamma^-=(1+\rho_\chi/\rho_\gamma)^{1/4}$}
If a nonrelativistic relic decays entirely into promptly thermalized photons, energy conservation at fixed <scale factor> gives $\rho_\gamma^+=\rho_\gamma^-+\rho_\chi^-$. Since thermal photons have $\rho_\gamma\propto T_\gamma^4$, their temperature rises by the displayed factor while an already decoupled <Cosmic neutrino background> is not heated. Before decay the relic-to-photon density ratio grows as $a$.
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