 Solution

ID: past-exam-of-the-general-relativity-and-cosmology-course-of-the-university-of-oxford/2013/3/b/solution

ρ_{M, 0} a^{- 3} = ρ_{R, 0} a^{- 4}

, so

a_{eq} = Ω_{R, 0} / Ω_{M, 0}

. Evaluating the integrated square-root relation gives

η_{eq} = \frac{2 ( 2 - 1 ) Ω _{R, 0}}{Ω _{M, 0} H _{0}} .

This assumes both present densities are positive and uses the same Big Bang origin for conformal time.

 New to topics? Read the docs here!