= Solution
The <Mészáros effect> suppresses the growth of modes which enter the horizon during <radiation domination>. Modes with comoving <wavenumber> $k\gg k_{\rm eq}$ enter earlier, but gain only a logarithmic growth factor until <matter-radiation equality>; modes entering during <matter domination> grow as $a$ after entry. Consequently small-scale amplitudes are reduced relative to an extrapolation of the unsuppressed large-scale <cosmological density power spectrum>, creating a turnover near the <matter-radiation equality scale> $k_{\rm eq}=\mathcal H_{\rm eq}$ in units $c=1$.
More quantitatively, for adiabatic primordial fluctuations with <scalar spectral index> $n_s$, the late-time linear spectrum can be written, up to a time-dependent normalization,
$$
P_m(k)\propto k^{n_s}T^2(k).
$$
The <cold-dark-matter transfer function> approaches a constant at $k\ll k_{\rm eq}$, whereas <logarithmic small-scale matter transfer> gives $T(k)\propto(k_{\rm eq}/k)^2\log(k/k_{\rm eq})$ at large $k$. Thus
$$
\boxed{P_m(k)\propto\begin{cases}k^{n_s},&k\ll k_{\rm eq},\\k^{n_s-4}\log^2(k/k_{\rm eq}),&k\gg k_{\rm eq}.\end{cases}}
$$
For approximately scale-invariant initial curvature fluctuations, $n_s\simeq1$, the large-$k$ scaling is $k^{-3}\log^2k$, rather than $k$. This discussion ignores baryonic acoustic structure and nonlinear clustering. The <Mészáros equation solution basis> includes both a constant and a logarithmic branch during radiation domination; the physical logarithmic growth is selected by matching the earlier radiation forcing, so not every mathematical solution grows logarithmically.
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