Temperature of a decoupled relativistic relic
= Temperature of a decoupled relativistic relic
If a relativistic species decouples when the coupled plasma has $g_{*s,\mathrm{dec}}$ entropy degrees of freedom, then after the plasma reaches $g_{*s}$ degrees of freedom,
$$
\frac{T_{\mathrm{relic}}}{T}
=\left(\frac{g_{*s}}{g_{*s,\mathrm{dec}}}\right)^{1/3}.
$$
The ratio follows from separate redshifting of the decoupled species and <cosmological entropy conservation> in the coupled plasma.