= Comoving momentum
{title2=$\mathbf q=a\mathbf p_{\rm phys}$}
= Canonical spatial momentum in an FRW universe
{synonym}
<Spatial translation> symmetry in a flat <FRW metric> conserves the covariant <canonical momentum> $q_i=ma^2dx^i/ds$ of a freely falling massive particle. An orthonormal spatial frame gives $p_{{\rm phys},i}=q_i/a$, so physical <momentum> <redshifts> as $a^{-1}$ even while the particle changes from relativistic to nonrelativistic motion. The local <energy> is $E=\sqrt{m^2+q^2/a^2}$ and the coordinate <velocity> is $d\mathbf x/dt=\mathbf q/[a\sqrt{q^2+m^2a^2}]$.
Back to article page
