General Relativity: An Introduction for Physicists · Problem 15.21

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · flat-matter-radiation-cosmic-time

Problem

For a spatially flat Friedmann model containing both matter and radiation, show that

H_0 t = \frac{2}{3\Omega_{\mathrm{m},0}^2}\left[(\Omega_{\mathrm{m},0}\, a + \Omega_{\mathrm{r},0})^{1/2}(\Omega_{\mathrm{m},0}\, a - 2\Omega_{\mathrm{r},0}) + 2\Omega_{\mathrm{r},0}^{3/2}\right].