Cosmology begins with a simple but profound idea: the Universe is not static. On large scales, distances between galaxies grow with time according to the scale factor $a(t)$. This is not galaxies moving through space in the usual sense; rather, space itself stretches. As a result, light traveling through the Universe is redshifted, and distant galaxies appear to recede faster the farther away they are.

The cosmological redshift is defined by $1+z = \frac{\lambda_{\rm obs}}{\lambda_{\rm emit}} = \frac{a(t_0)}{a(t_{\rm emit})}$. For nearby galaxies, the recession speed obeys Hubble's law, $v = H_0 d$, where $H_0$ is the Hubble constant. At sufficiently large distances, however, the simple linear law becomes only an approximation because the expansion rate changes with time and light takes a long time to travel.