 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/9d/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

When

Γ ≫ 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}, s a^{3} = constant,

one gets

T^{3} a^{3} = constant

and hence

T \propto a^{- 1}

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