Primordial black holes from the perturbations in the inflaton potential

Abstract

A perturbation in the inflaton potential can lead inflation into the ultra-slow-roll stage. The power spectrum of primordial curvature perturbation is thus substantially enhanced, generating abundant primordial black holes on small scales. In this paper, the power spectra are numerically calculated in the single-field inflation model, with one or two perturbations in the inflaton potential. The form of perturbation is constructed in an antisymmetric way, so that the inflaton neither rolls down rapidly after the ultra-slow-roll stage nor even stops in the ultra-slow-roll region. The primordial black holes with the abundance around 0.1 in one or two typical mass windows at 1 0 − 17 M ⊙ , 1 0 − 13 M ⊙ , and 30 M ⊙ can be achieved, without spoiling the nearly scale-invariant power spectrum on large scales.