Primordial black holes from metric preheating: mass fraction in the excursion-set approach

TL;DR

This paper calculates the primordial black hole mass distribution resulting from metric preheating after inflation, using an improved excursion-set approach to account for the cloud-in-cloud mechanism, revealing a peak mass range from grams to stellar masses.

Contribution

It introduces a singularity-free Volterra integral equation within the excursion-set framework to better compute PBH mass distributions from metric preheating.

Findings

PBHs can dominate the universe if the instability stops early enough.

The mass distribution peaks well above the Hubble mass at inflation's end.

The peak mass ranges from 10 grams to stellar masses, affecting cosmological scenarios.

Abstract

We calculate the mass distribution of Primordial Black Holes (PBHs) produced during metric preheating. After inflation, the oscillations of the inflaton at the bottom of its potential source a parametric resonant instability for small-scale scalar perturbations, that may collapse into black holes. After reviewing in a pedagogical way different techniques that have been developed in the literature to compute mass distributions of PBHs, we focus on the excursion-set approach. We derive a Volterra integral equation that is free of a singularity sometimes encountered, and apply it to the case of metric preheating. We find that if the energy density at which the instability stops, $\rho_\Gamma$, is sufficiently smaller than the one at which inflation ends, $\rho_\mathrm{end}$, namely if $\rho_\Gamma^{1/4}/\rho_\mathrm{end}^{1/4}< 10^{-5}(\rho_\mathrm{end}^{1/4}/10^{16}\mathrm{GeV})^{3/2}$, then PBHs dominate the universe content at the end of the oscillatory phase. This confirms the previous analysis of arXiv:1907.04236 . By properly accounting for the "cloud-in-cloud" mechanism, we find that the mass distribution is more suppressed at low masses than previously thought, and peaks several orders of magnitude above the Hubble mass at the end of inflation. The peak mass ranges from $10$ g to stellar masses, giving rise to different possible cosmological effects that we discuss.