Clustering of Primordial Black Holes in Excursion Set Theory

TL;DR

This paper extends Excursion Set Theory to analyze the clustering behavior of Primordial Black Holes, revealing how spectral index and density thresholds influence their formation and spatial distribution.

Contribution

It introduces a novel EST-based framework to compute PBH pair probabilities and clustering, linking spectral properties to clustering outcomes.

Findings

Enhanced power spectrum increases PBH formation and clustering.

Blue-tilted spectral index correlates with specific mass ranges for PBH formation and clustering.

Clustering probability decreases with larger clustering distances and higher density thresholds.

Abstract

We investigate the clustering of Primordial Black Holes (PBHs) within the framework of Excursion Set Theory (EST). The EST formalism is extended to compute the joint probability of forming PBH pairs within a clustering distance, based on two stochastic trajectories with a shared history. Our results show that an enhanced power spectrum not only increases the formation of PBHs in specific mass ranges but also enhances their clustering probability. We find a one-to-one correspondence between the blue-tilted spectral index and the mass ranges in which PBHs form and cluster. Additionally, we demonstrate that the clustering probability decreases asymptotically with increasing clustering distance, while a higher critical density threshold (barrier) leads to a suppression of clustering abundance.