General Relativity: An Introduction for Physicists · Problem 15.18

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · einstein-de-sitter-model-results

Problem

For the Einstein--de Sitter model, prove the following useful results:

a(t) = \left(\frac{t}{t_0}\right)^{2/3}, \qquad H(t) = \frac{2}{3t} = H_0(1+z)^{3/2}, \qquad q_0 = \frac{1}{2}, \qquad \rho_m(t) = \frac{1}{6\pi G t^2}.