Cosmic-time matter density modes
= Cosmic-time matter density modes
In cosmic time during matter domination, $a(t)\propto t^{2/3}$ and the pressureless density contrast obeys
$$
\ddot\delta+\frac4{3t}\dot\delta-\frac2{3t^2}\delta=0.
$$
Its growing and decaying solutions are $t^{2/3}$ and $t^{-1}$.