Solution
= Solution
During matter domination, $a\propto t^{2/3}$, $H=2/(3t)$ and $4\pi G\bar\rho_m=2/(3t^2)$. Trying $\delta_m=t^p$ gives
$$
p(p-1)+\frac43p-\frac23=0,
$$
with roots $p=2/3,-1$. The growing <linear cosmological density perturbation> is therefore
$$
\boxed{\delta_m\propto t^{2/3}\propto a}.
$$