= Physical momentum in an FRW universe
{title2=$\mathbf p_{\rm phys}=m\gamma\mathbf v=\mathbf q/a$}
= Physical momenta in an FRW universe
{synonym}
A freely falling particle's physical <momentum> is measured in the local <orthonormal frame> of a <comoving observer>. With proper <peculiar velocity> $\mathbf v=a\,d\mathbf x/dt$ and <Lorentz factor> $\gamma=(1-v^2)^{-1/2}$, it is $m\gamma\mathbf v$. It differs by one factor of the <scale factor> from the conserved <comoving momentum>. For a <nonrelativistic particle>, its <peculiar velocity> therefore decays as $a^{-1}$.
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