Are primordial black holes produced by entropy perturbations in single field inflationary models?

Understand

We show that in single field inflationary models the super-horizon evolution of curvature perturbations on comoving slices $\mathcal{R}$, which can cause the production of primordial black holes (PBH), is not due to entropy perturbations, but to the background evolution effect on the conversion between entropy and curvature perturbations.

• We derive a general relation between the time derivative of comoving curvature perturbations and entropy perturbations, in terms of a conversion factor depending on the background evolution.
• Contrary to previous results derived in the uniform density gauge assuming the gradient term can be neglected on super-horizon scales, the relation is valid on any scale for any minimally coupled single scalar field model, also on sub-horizon scales where gradient terms are large.
• We apply it to the case of quasi-inflection inflation, showing that while entropy perturbations are decreasing, $\mathcal{R}$ can grow on super-horizon scales, due to a large increase of the conversion factor.