 Solution

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

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

R_{α β γ δ} R^{α β γ δ} = 12 [(\frac{a ¨}{a})^{2} + (\frac{a ˙ ^{2} + k}{a ^{2}})^{2}] .

With

a = t

and

k = - 1

, both terms vanish, so

R_{α β γ δ} R^{α β γ δ} = 0 .

Indeed the vacuum equations give a vanishing Ricci tensor, and conformal flatness of an FLRW metric then makes the whole Riemann tensor vanish. The apparent singularity at

t = 0

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