= Density bound on a relativistically decoupled massive relic
{title2=$m_x\lesssim\frac{\Omega_{x,\max}}{\Omega_\gamma}\frac{\langle E_\gamma\rangle}{n_x/n_\gamma}$}
A species freezing out while relativistic retains its thermal comoving number. If it is nonrelativistic today, $\rho_x\simeq m_xn_x$. Comparing with <photons> gives $\Omega_x/\Omega_\gamma=m_x(n_x/n_\gamma)/\langle E_\gamma\rangle$. An upper density fraction therefore bounds its mass inversely with its relic number density. The relation does not apply unchanged to a species whose abundance is depleted by nonrelativistic annihilation.
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