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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.

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

where:

<math>L</math> = physical distance

<math>\lambda</math> = a distance in comoving units

<math>a(t)</math> ( lub <math>S(t)</math> ) - 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

<math> a(t_0) = 1</math> where <math>t_0</math> 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.