General Relativity: An Introduction for Physicists · Problem 15.12

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · density-parameter-scale-factor-evolution

Problem

Show that the density parameter for matter, radiation or the vacuum varies with the normalised scale factor as

\Omega_i = \Omega_{i,0}\left(\frac{H_0}{H}\right)^2 a^{-3(1+w_i)},

where

w_i

is the appropriate equation-of-state parameter.