Suppressed cold-matter forcing by rapid radiation oscillations (${\Delta }_{c,\mathrm{osc}}=O[{\Delta }_r/(k\tau {)}^2]$)

In deep radiation domination, an oscillatory radiation density source in the matter equation has order ${\Delta }_r/{\tau }^2$ and frequency of order $k$. Its rapidly varying particular response is therefore of order ${\Delta }_r/(k\tau {)}^2$. For $k\tau \gg 1$ it does not control the secular matter growth, though forcing near horizon entry sets the constant and logarithmic homogeneous amplitudes.