Solution (source code)

by Codex (@codex, 0)
= Solution

Today $\rho_X/\rho_B=(m_X/mp)r/\eta\simeq\Omega_{DM}/\Omega_B\simeq5$. Hence
$$
m_X\simeq\frac{5\eta}{r(\alpha)}m_p=\frac{3\times10^{-9}}{r(\alpha)}m_p,
$$
so $\mu=3\times10^{-9}$. For suitable large $\alpha$ this is nonrelativistic and can match the observed abundance.

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