# cosmic scale factor

## cosmic scale factor

Symbol:*R.*A measure of the size of the Universe as a function of time.

*R*is related to the redshift parameter,

*z,*by

1 +

*z*=*R*(*t*_{0})/*R*(*t*_{1})where *t *_{0} is the present time and *t *_{1} is the time at emission of the radiation. The quantity (1 + *z*) thus gives the factor by which the Universe has expanded in size between the time *t *_{1} and the present, *t *_{0}. The *proper distance* between the origin and a point at a comoving coordinate *r * (i.e. in a system expanding with the Universe) is given by the product of *R *(*t*) and sin^{–1}*r, r, * or sinh^{–1}*r * depending on whether the Universe is closed, Euclidean, or open, respectively. *R * is also related to the Hubble constant *H *_{0} :

*H*

_{0}=

*R*

^{–1}(d

*R*/d

*t*)

Collins Dictionary of Astronomy © Market House Books Ltd, 2006