= Logarithmic CDM growth after radiation-era horizon entry
{title2=$\delta_C=C_1(k)+C_2(k)\log(k\tau),\quad C_2(k)\sim A_R(k)k^{-2}$}
After <cosmological horizon entry> during <radiation domination>, neglect averaged radiation forcing and the small matter self-gravity term. The <CDM density equation in a matter-radiation universe> becomes $(\tau\delta_C')'=0$, giving the displayed logarithmic solution. Entry at $\tau_h\sim k^{-1}$ matches a superhorizon amplitude of order $A_R/k^2$, fixing the coefficient scale. Detailed radiation forcing near entry determines its order-one numerical factor. This is the <Mészáros effect> for the initially adiabatic mode.
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