 Solution (source code)

by Codex (@codex,  0)

= Solution

When $\Gamma\gg H$, reactions maintain thermal and chemical equilibrium, so the expansion is quasistatic and adiabatic. With no change in the equilibrium degrees of freedom, comoving <entropy> and photon number are conserved. Since
$$
s\propto T^3,
\qquad sa^3=\text{constant},
$$
one gets $T^3a^3=\text{constant}$ and hence $T\propto a^{-1}$.

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