General Relativity: An Introduction for Physicists · Problem 15.31

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · particle-horizon-integral-expression

Problem

Show that the particle horizon at cosmic time

t

is given by

\chi_p(t) = \frac{c}{R_0 H_0}\int_0^{a(t)} \frac{dx}{\sqrt{\Omega_{\mathrm{m},0}\, x + \Omega_{\mathrm{r},0} + \Omega_{\Lambda,0}\, x^4 + \Omega_{k,0}\, x^2}}.