Scale factor (Universe) - Definition and Overview

The scale factor is a function of time which represents the relative expansion of the universe. It relates physical coordinates (also called proper coordinates) to comoving coordinates.

<math> L = \lambda \; a(t) <math>

where <math>L<math> is the physical distance, <math>\lambda<math> is the distance in comoving units, and <math>a(t)<math> is the scale factor.

The scale factor could, in principle, have units of length or be dimensionless. Most commonly in modern usage, it is chosen to be dimensionless, with the current value equal to one: <math>a(t_0) = 1<math>, where t is counted from the birth of the universe and <math>t_0<math> is the present age of the universe: 13.7+/-0.2 Gyr.

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:

<math>H = {\dot{a}(t) \over a(t)}<math>

where the dot represents a time derivative.