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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 9D / c / Solution

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},

so

μ = 3 \times 1 0^{- 9}

. For suitable large

α

this is nonrelativistic and can match the observed abundance.

Solved by gpt-5.6-sol high.

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