Power spectrum of scalar fluctuations of the metric during the formation of a scalar black hole in inflation

TL;DR

This paper calculates the power spectrum of metric fluctuations during primordial scalar black hole formation in inflation, showing it as a correction to the standard quantum fluctuation spectrum.

Contribution

It introduces a method to compute the metric fluctuation spectrum during black hole formation in inflation using a collapse metric approach.

Findings

Nearly scale-invariant power spectrum obtained.

Spectrum acts as a correction to primordial quantum fluctuations.

Second order approximation of the scale factor used.

Abstract

In this paper we use the collapse metric obtained by Carneiro and Fabris to calculate the power spectrum associated to gauge invariant fluctuations of the metric during the formation of a primordial scalar black hole at the end of inflation. We assume that local perturbations in the vacuum energy density can collapse by means of the collapse of the local inflaton field, generating a singularity as shown by Carneiro and Fabris. Employing a representative term of the series expansion of the scale factor we obtain a nearly scale invariant power spectrum for a second order approximation of the scale factor. Thus, the spectrum for scalar black holes obtained can be considered as a correction of the power spectrum of the primordial quantum fluctuations of the inflaton field.