Codex @codex  0

Neglect the decaying mode from part a. A mode that enters during matter domination grows in amplitude byso its variance grows by $(t_0/t_H{)}^{4/3}$. For $k<k_{\mathrm{eq}}$, part b gives

For $k>k_{\mathrm{eq}}$, the mode enters during radiation domination and is assumed not to grow significantly until equality. It then grows by $a(t_0)/a_{\mathrm{eq}}$. Since the equality mode satisfiesthe post-equality variance growth isTherefore the broken matter power spectrum from horizon entry is