= Temperature ratio of an early-decoupled neutrino
{title2=$T_X/T_\gamma=[43/(11g_{*s,D})]^{1/3}$}
A relativistic species decoupling before ordinary <neutrino decoupling> cools as $T_X\propto a^{-1}$. <Cosmological entropy conservation> in the remaining bath gives $T_X/T_\nu=[10.75/g_{*s,D}]^{1/3}$, where $g_{*s,D}$ counts that bath just after the early species has left it. Subsequent <electron-positron annihilation in cosmology> gives $T_\nu/T_\gamma=(4/11)^{1/3}$. For the ideal high-temperature <relativistic entropy content of the Standard Model>, the resulting ratio is about $0.332$.
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