Sharp-equality cold-dark-matter transfer approximation (source code)

= Sharp-equality cold-dark-matter transfer approximation
{title2=$T_\delta(k)\sim\begin{cases}k^2\tau_0^2/10&k\ll k_{\rm eq},\\k_{\rm eq}^2\tau_0^2/10&k\gg k_{\rm eq}.\end{cases}$}

In the idealization that subhorizon cold matter freezes during <radiation domination>, early-entering modes have an entry density of order the primordial curvature, retain it until equality, and then share the same matter-era growth factor. Their density-per-curvature transfer becomes approximately independent of $k$. Matching this plateau to the matter-era $k^2$ transfer gives the displayed sharp-transition model, with its high-$k$ coefficient dependent on the matching convention. A scale-invariant curvature spectrum then gives density power proportional to $k$ below equality and $k^{-3}$ above it. Actual cold matter grows logarithmically in the radiation era, adding the familiar high-$k$ logarithms of the <Mészáros effect>.