On primordial black holes from an inflection point

Understand

Recently, it has been claimed that inflationary models with an inflection point in the scalar potential can produce a large resonance in the power spectrum of curvature perturbation.

• In this paper however we show that the previous analyses are incorrect.
• The reason is twofold: firstly, the inflaton is over-shot from a stage of standard inflation and so deviates from the slow-roll attractor before reaching the inflection.
• Secondly, on the (or close to) the inflection point, the ultra-slow-roll trajectory supersede the slow-roll one and thus, the slow-roll approximations used in the literature cannot be used.