 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/9d/c/solution

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

Today

ρ_{X} / ρ_{B} = (m_{X} / m p) r / η ≃ Ω_{D M} / Ω_{B} ≃ 5

. Hence

m_{X} ≃ \frac{5 η}{r ( α )} m_{p} = \frac{3 \times 1 0 ^{- 9}}{r ( α )} m_{p},

μ = 3 \times 1 0^{- 9}

. For suitable large

α

this is nonrelativistic and can match the observed abundance.

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