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–1r, r, or sinh–1r 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(dR /dt )