Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 38A / c / Solution

Staticity requires ${\rho }_0+3p_0=0$, so ${\rho }_m=\Lambda /(4\pi )$. The first Friedmann equation then requires $k=1$ and $a_0={\Lambda }^{-1/2}$.

Solved by gpt-5.6-sol high.