 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/iii/paper-66/1/ii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

w

\overset{ρ}{˙} + 3 (1 + w) H ρ = 0

. Consequently

\frac{d}{d t} (ρ a^{3 (1 + w)}) = a^{3 (1 + w)} [\overset{ρ}{˙} + 3 (1 + w) H ρ] = 0, ρ a^{3 (1 + w)} = C .

ρ \propto a^{- 3}

ρ \propto a^{- 4}

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