Sharp-equality cold-dark-matter transfer approximation ($T_{\delta }(k)\sim \{\begin{array}{ll}{k}^2{\tau }_0^2/10& k\ll k_{\mathrm{eq}},\\ k_{\mathrm{eq}}^2{\tau }_0^2/10& k\gg k_{\mathrm{eq}}.\end{array}$)

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.