Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 310 / 4 / e / ii / Solution

The dominant component is smooth, so only the subdominant matter density clusters. The cold-matter perturbation equation is thereforeAt late times, $a\gg 1$, the source term is negligible compared with the expansion terms. Setting $\tau =t-t_{\ast }$ and using $H=2/\tau$ givesIt integrates toThe constant mode shows the suppression of matter growth by smooth accelerated expansion; the second mode decays.

Solved by gpt-5.6-sol high.