 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/38d/a/solution

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

For

k = - 1

d s^{2} = - d t^{2} + a^{2} (t) [d χ^{2} + sinh^{2} χ (d θ^{2} + sin^{2} θ d ϕ^{2})] .

Λ = 0

, gives

\frac{a ˙ ^{2} - 1}{a ^{2}} = 0.

Choosing the expanding branch and shifting the origin of proper time yields

a (t) = t, t > 0 .

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