 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/14d/a/i/solution

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

r = a (q + ψ)

to first order gives

x^{''} + H x^{'} ≃ ψ^{''} + H ψ^{'} = - \nabla_{q} φ

. The perturbation of Poisson's equation is

\nabla_{q}^{2} φ = (4 π G / c^{2}) a^{2} \overset{ρ}{ˉ}_{M} δ_{M}

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