 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-2/9b/d/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

a^{- 3}

. Hence

ρ_{dust} (a) = ρ_{cc} (\frac{a _{eq}}{a})^{3} .

The transition occurs when

ρ + 3 P = ρ_{dust} - 2 ρ_{cc} = 0

, so

(\frac{a _{eq}}{a})^{3} = 2, \frac{a}{a _{eq}} = 2^{- 1/3} .

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