= Matter-era density transfer from primordial curvature
{title2=$\delta_c(k,\tau)=\frac{k^2\tau^2}{10}\zeta_*(k)$}
For the regular growing mode in a purely matter-dominated flat background, $h=-2\delta_c$ and $\delta_c=C\tau^2$. The synchronous Einstein constraint $\mathcal Hh'+k^2h^-/3=3\mathcal H^2\delta_c$ with $\mathcal H=2/\tau$ gives $h^-=60C/k^2$. Hence $\zeta=h^-/6+\delta_c/3=10C/k^2+C\tau^2/3$, conserved to leading order on <superhorizon scales>. Identifying its early constant value gives the displayed density transfer; it includes a $k^2$ factor that is factored out of the conventionally normalized matter transfer function.
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