= Superhorizon growing density mode of adiabatic matter and radiation
{title2=$\Delta_c\propto\tau^2$}
An adiabatic perturbation obeys $\Delta_r=(4/3)\Delta_c$. In a radiation background this makes the cold-matter density equation $\Delta_c''+\Delta_c'/\tau=4\Delta_c/\tau^2$, whose growing solution is $\tau^2$. In a matter background it instead becomes $\Delta_c''+2\Delta_c'/\tau=6\Delta_c/\tau^2$, with the same growing conformal-time exponent and a different scale-factor dependence.
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