= Frozen-radiation approximation to the matter transfer function
{title2=$T(k)=G\min\{1,(k_{\rm eq}/k)^2\}$}
Assume all relevant modes begin outside the horizon at common <conformal time> $\tau_i$, grow as $\tau^2$ until radiation-era horizon entry, then freeze until <matter-radiation equality>, and again grow as $\tau^2$ in matter domination. With horizon entry $\tau_h=2\pi/k$, $k_{\rm eq}=2\pi/\tau_{\rm eq}$ and final time $\tau_0$, direct multiplication of the growth factors gives the displayed transfer with $G=(\tau_0/\tau_i)^2$. A primordial density <power spectrum> $P_i=Ak$ becomes $P_0=AG^2k$ below equality wavenumber and $AG^2k_{\rm eq}^4k^{-3}$ above it. This approximation neglects the true logarithmic radiation-era matter growth, baryonic acoustic structure and late acceleration; a conventionally normalized transfer divides out $G$.
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