Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 73 / 2 / i / Solution

Divide the Friedmann equation by $a^2$ and use $a=(1+z{)}^{-1}$. The Hubble parameter therefore satisfiesThe positive root describes the expanding branch. Spatial flatness and the neglect of radiation in cosmology imply ${\Omega }_{m,0}+{\Omega }_{\Lambda ,0}=1$.