Broken matter power spectrum from horizon entry
= Broken matter power spectrum from horizon entry
If primordial horizon-crossing perturbations satisfy $V\langle|\delta_k|^2\rangle=C/k^3$, remain frozen during radiation domination, and grow as $a$ during matter domination, then
$$
P(k)=
\begin{cases}
Ck/k_0^4,&k<k_{\rm eq},\\
Ck_{\rm eq}^4/(k^3k_0^4),&k>k_{\rm eq}.
\end{cases}
$$