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

TL;DR

This paper demonstrates how to reconstruct inflationary potentials from specific primordial power spectra, highlighting the non-uniqueness of such reconstructions in multi-field models with peaks on small scales.

Contribution

It introduces a method to reconstruct inflation potentials from power spectra with large-scale scale invariance and small-scale peaks, considering multi-field inflation complexities.

Findings

Potential reconstruction from power spectra is feasible.

Multiple potentials can correspond to the same power spectrum.

Reconstruction reveals non-uniqueness in multi-field inflation models.

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 multi-filed inflation models, the curved trajectory of the scalar fields in the field space can generate a peak in the power spectrum on small scales due to the existence of the isocurvature perturbation. Here we show that a potential can be reconstructed from a given power spectrum, which is made of a scale-invariant one on large scales and the other function with a peak on small scales. In multi-field inflation models the reconstructed potential may not be unique and we can find different potentials from a given power spectrum.