Scale factor

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:

= physical distance
= a distance in comoving units
( lub ) - the scale factor

The scale factor could in principle either have length units or be dimensionless.

Most commonly in modern usage, it is chosen to be dimensionless, with

where

is the present age of the Universe.

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.