= Expansion-weighted derivative of a passive density perturbation
{title2=$a^2\dot\delta=\mathrm{constant}$}
When the self-gravity source in the pressureless <linear cosmological density perturbation> equation is negligible, $\ddot\delta+2(\dot a/a)\dot\delta=0$. Multiplication by $a^2$ makes it $d(a^2\dot\delta)/dt=0$, so $\delta=C_1+C_2\int dt/a^2(t)$. This explains how <Hubble friction> changes growth for an arbitrary positive <scale factor>. For $a\propto t^p$, the nonconstant mode is $t^{1-2p}$ when $p\ne1/2$ and $\log t$ when $p=1/2$.
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