The scale factor is a variable which represents the relative expansion of the Universe. It relates physical coordinates (also called proper coordinates) to comoving coordinates.
where:
Most commonly in modern usage, it is chosen to be dimensionless, with
The evolution of the scale factor is a dynamical question, determined by the equations of general relativity, which are presented in the case of a locally isotropic, locally homogeneous universe by the Friedmann equations.
The Hubble parameter is defined:
where the dot represents a time derivative.