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 )

Collins Dictionary of Astronomy © Market House Books Ltd, 2006