Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 1 / 9E / b / Solution

Each photon loses a factor $(1+z{)}^{-1}$ in energy, and cosmological time dilation reduces the photon arrival rate by another factor $(1+z{)}^{-1}$. Henceso $n=2$. The physical area of the sphere today is $4\pi a(t_0{)}^2{x}^2$, giving flux

Solved by gpt-5.6-sol high.