General Relativity: An Introduction for Physicists · Problem 15.29

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · density-parameter-time-evolution

Problem

For a general cosmological model, show that

\dot{\Omega}_i = \Omega_i H(\Omega_m + 2\Omega_r - 2\Omega_\Lambda - 1 - 3w_i),

where

i

denotes matter, radiation or the vacuum.