Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 9D / b / 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. Sinceone gets $T^3{a}^3=\text{constant}$ and hence $T\propto a^{-1}$.