# Primordial Black Holes from Broad Spectra: Abundance and Clustering

## TL;DR

This paper investigates the formation and distribution of primordial black holes generated by broad scalar perturbation spectra during inflation, concluding they are rare, predominantly Poissonian, and have similar mass distributions to narrow spectra.

## Contribution

It provides a detailed analysis of primordial black hole formation and clustering for broad spectra, showing the rarity of their formation and their mostly Poissonian distribution.

## Key findings

- Primordial black holes from broad spectra are rare events.
- Their mass distribution is similar to that from narrow spectra.
- They are not significantly clustered at formation, with a Poissonian distribution.

## Abstract

A common mechanism to form primordial black holes in the early universe is by enhancing at small-scales the scalar perturbations generated during inflation. If these fluctuations have a large enough amplitude, they may collapse into primordial black holes upon horizon re-entry. Such primordial black holes may comprise the totality of the dark matter. We offer some considerations about the formation and clustering of primordial black holes when the scalar perturbations are characterised by a broad spectrum. Using the excursion set method, as well as the supreme statistics, we show that the cloud-in-cloud phenomenon, for which small mass primordial black holes may be absorbed by bigger mass ones, is basically absent. This is due to the fact that the formation of a primordial black hole is an extremely rare event. We also show that, from the point of view of mass distribution, broad and narrow spectra give similar results in the sense that the mass distribution is tilted towards a single mass. Furthermore, we argue that primordial black holes from broad spectra are not clustered at formation, their distribution is dominantly Poissonian.