= Solution
Let $k_{\rm eq}$ be the horizon scale at <matter-radiation equality>. At a fixed time soon after recombination, the <cold-dark-matter transfer function> defined as $T_c=\Delta_c/\mathcal R$ has the schematic behavior
$$
T_c(k)\propto
\begin{cases}
k^2,&k\ll k_{\rm eq},\\
\log(k/k_{\rm eq}),&k\gg k_{\rm eq},
\end{cases}
$$
with a smooth turnover near $k_{\rm eq}$. Large-scale modes enter the horizon during matter domination and the <Poisson equation> converts an almost scale-independent primordial potential into a density contrast proportional to $k^2$. Small-scale modes enter during radiation domination; radiation controls the potential and pressure prevents it from clustering, so cold-dark-matter growth is only logarithmic until equality. Subsequent matter-era growth multiplies all these modes by the same <linear growth factor>.
Equivalently, if the conventional matter transfer function is normalized to one as $k\to0$, it is constant for $k\ll k_{\rm eq}$ and falls approximately as $\log(k/k_{\rm eq})/k^2$ for $k\gg k_{\rm eq}$. Multiplication by the Poisson factor $k^2$ gives the behavior of the definition used here.
Back to article page
