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The scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor.[1] It relates the comoving distances for an expanding universe with the distances at a reference time arbitrarily taken to be the present.

l_p = l_t \; a(t)

where \! l_t is the comoving distance at epoch \! t, \! l_p is the distance at the present epoch \! t_p and \! a(t) 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: \! a(t_p) = 1, where \! t is counted from the birth of the universe and \! t_p is the present age of the universe: 13.7\pm0.2\,\mathrm{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:

H \equiv {\dot{a}(t) \over a(t)}

where the dot represents a time derivative.


  1. ^ Steven Weinberg (2008). Cosmology. Oxford University Press. p. 3. ISBN 9780198526827.  

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