Superpotential method and the amplification of inflationary perturbations

TL;DR

This paper uses the superpotential method to reconstruct inflaton potentials that amplify curvature perturbations, potentially leading to primordial black hole formation, across various gravity theories.

Contribution

It applies the superpotential method to different gravity models to identify features that enhance scalar spectrum and promote primordial black hole formation.

Findings

Amplification of curvature perturbations can be achieved with specific inflaton potential features.

The method is effective across minimally coupled, nonminimal, and $f(R)$ gravity theories.

Models show potential for primordial black hole formation after inflation.

Abstract

The superpotential method is a reconstruction technique which has proven useful to build exact cosmological solutions. We here employ the superpotential method in order to reconstruct the features necessary for the inflaton potential to drive inflation and lead to the amplification of the curvature perturbations. Such an amplification, at wavelengths shorter than those observed in the cosmic microwave background, is necessary in order to have a significant formation of primordial black holes after inflation ends. The technique is applied to the cases of a minimally coupled inflaton, to the nonminimal coupling case and to $f(R)$ theories of gravity. For such theories, a model dependent analysis of the features leading to the scalar spectrum enhancement is also presented.