= Monotonic photon cooling during pair annihilation
{title2=$d\ln T_\gamma/d\ln a=-3/[3+d\ln g_{*s}/d\ln T_\gamma]$}
Electromagnetic comoving <entropy> conservation gives $a^3g_{*s}(T_\gamma)T_\gamma^3$ constant. Differentiation proves the displayed relation. During equilibrium electron-positron annihilation, $g_{*s}$ increases with <temperature>, so the absolute <photon> <temperature> still falls as space expands. The comoving <temperature> $aT_\gamma$ rises, and the asymptotic relativistic-to-pair-free <entropy> count heats <photons> relative to decoupled <neutrinos> by $(11/4)^{1/3}$. This relative heating must not be mistaken for an absolute <temperature> rise along the smooth expanding history.
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