Clustering of Primordial Black Holes in Excursion Set Theory

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.