The
scale factor,
cosmic scale factor or sometimes the
Robertson-Walker scale factor parameter of the
Friedmann equations is a function of time which represents the
relative expansion of the
universe. It relates the proper distance (which can change over time, unlike the
comoving distance which is constant) between a pair of objects, e.g. two galaxy clusters, moving with the Hubble flow in an expanding or contracting
FLRW universe at any arbitrary time
to their distance at some reference time
. The formula for this is:
where
is the proper distance at epoch
,
is the distance at the reference time
and
is the scale factor. Thus, by definition,
.