= Matching the CDM growing mode at horizon entry
{title2=$\delta_C=\frac{A_R}{k^2}[1+2\log(k\tau)]\quad(\tau\ge k^{-1})$}
In an instantaneous-transition approximation, match the <superhorizon adiabatic CDM mode in radiation domination> and its first derivative to the radiation-era logarithmic solution at $\tau_h=1/k$. Its value is $A_R/k^2$ and its derivative is $2A_R/k$. The two matching equations give the displayed expression. Its coefficient two belongs to this approximation; a smooth radiation forcing through entry changes the constants while preserving the <logarithmic CDM growth after radiation-era horizon entry> scaling.
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