## Encyclopedia > Scale factor

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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.

$L = \lambda \; a(t)$

where:

• $L$ = physical distance

• $\lambda$ = a distance in comoving units

• $a(t)$ ( lub $S(t)$ ) - 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

$a(t_0) = 1$
where $t_0$ 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:

${\dot{a}(t) \over a(t)}$

where the dot represents a time derivative.

All Wikipedia text is available under the terms of the GNU Free Documentation License

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