At a fixed cosmological time, homogeneous expansion has $\mathbf v=H(t)\mathbf r$. A comoving galaxy has $\mathbf r=R(t)\mathbf x$ with constant $\mathbf x$, hence $\mathbf v=\dot R\mathbf x=(\dot R/R)\mathbf r$. Thus $\boxed{H=\dot R/R}$. Peculiar velocities must be removed before applying this ideal relation to individual galaxies.


Solution

Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S2 / 3 / 1 / Solution

 Solution (source code)