= Solution
<cold dark matter> is nonrelativistic and effectively collisionless on the scales of interest. Its small <velocity dispersion> limits <free streaming>, allowing small-scale gravitational wells to survive. <baryons> coupled to <photons> undergo acoustic motion and damping before <recombination>; <dark matter> does not share that <photon> <pressure>, and provides potential wells into which <baryons> can later fall.
For a subhorizon pressureless perturbation, once a Newtonian treatment is applicable,
$$
\ddot\delta+2H\dot\delta-4\pi G\bar\rho_m\delta=0.
$$
During <radiation domination> the matter contribution to the background gravity is small; neglecting it gives $\delta\simeq C_1+C_2\log t$. This slow subhorizon growth is the <Mészáros effect>. During <matter domination>,
$$
\boxed{\delta=C_+a+C_-a^{-3/2}}
$$
in an <Einstein-de Sitter universe>. Once $\delta$ approaches unity, linear theory fails and collapse, <virialization> and merging become important.
Modes entering the horizon during <radiation domination> therefore grow less before equality than longer modes entering later. This scale dependence is encoded in a <transfer function>, with a schematic linear <matter power spectrum> $P(k,a)=A k^{n_s}T^2(k)D^2(a)$. <cold dark matter> supports hierarchical assembly; a sufficiently large warm- or hot-dark-matter free-streaming length suppresses small-scale structure. Superhorizon <density contrasts> change under a <gauge transformation in cosmological perturbation theory>, so the subhorizon growth laws should not be applied indiscriminately outside the horizon. The original cold-dark-matter formation model explicitly connects weak <free streaming> to the spectrum that seeds galaxies and clusters.<Formation of galaxies and large-scale structure with cold dark matter by George R. Blumenthal and others>[1984, Nature 311, pp. 517–525, abstract: collisionless cold particles, retained fluctuations and the post-recombination spectrum]{ref}
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