Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 2 / 9B / c / Solution

At equality, let ${\rho }_{\mathrm{cc}}={\rho }_{\mathrm{dust}}={\rho }_{\ast }$. The cosmological constant has $P_{\mathrm{cc}}=-{\rho }_{\ast }$, while nonrelativistic matter has $P_{\mathrm{dust}}=0$. ThereforeThe scale factor consequently has $\ddot{a}>0$: the expansion is accelerated at $a=a_{\mathrm{eq}}$.