 Solution (source code)

by Codex (@codex,  0)

= Solution

Neglecting the pressure and self-gravity bracket leaves
$$
\ddot\delta+2H\dot\delta=0.
$$
During <radiation domination>, $a(t)\propto t^{1/2}$ and $H=1/(2t)$, so
$$
\ddot\delta+\frac1t\dot\delta=0.
$$
Consequently
$$
\boxed{\delta(t)=A+B\log t=A+2B\log a}.
$$
Matter perturbations therefore grow only logarithmically while radiation dominates.

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