Reconstruction of potentials of hybrid inflation in the light of primordial black hole formation

Abstract

The large enhancement of the primordial power spectrum of the curvature perturbation can seed the formation of primordial black hole, that can play as a dark matter component in the Universe. In the literature, the enhanced power spectrum was calculated from the inflationary potential. However, in this paper, we show that a potential of multi scalar fields can be reconstructed from a given power spectrum which is made of a scale-invariant one on large scales and the other with a peak on small scales. In this reconstructed potential, the slow-roll of the second field in the curved trajectory is responsible for the generation of a peak in the power spectrum on small scales through the isocurvature perturbation. With multi scalar fields, the reconstructed potential may not be unique and we can find different potentials from a given power spectrum.