Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 14D / iii / Solution

Under the stated approximation the perturbation equation isDuring radiation domination, $a\propto t^{1/2}$, so $\dot{\delta }\propto t^{-1}$ andMatter perturbations therefore have only logarithmic growth of matter perturbations during radiation domination.

In a curvature-dominated universe, $a\propto t$, so $\dot{\delta }\propto t^{-2}$ andThe nondecaying mode is constant: curvature domination gives freezing of matter perturbations during curvature domination, rather than continued growth.