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Hubble's law $$ v=H_0 d,$$ relates the recession velocity $v$ of a distant object to it's physical distance $d$. Today, the physical distance coincides, by definiton, to the comoving distance $\chi \equiv d/(1+z)$, but if you want to know how fast two galaxies at a redshift of, say, $z=1$, you must plug in their physical distance at that time (and use $H(z)$,...


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