Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects

Understand

Using an excursion-set approach, we revisit the initial spatial clustering of Primordial Black Holes (PBHs) originating from the Hubble re-entry of large Gaussian density fluctuations in the early universe.

• We derive the two-point correlation functions of PBHs, properly accounting for the "cloud-in-cloud" mechanism.
• Our expressions naturally and intrinsically correlate the formation of pairs of PBHs, which is a key difference with the Poisson model of clustering.
• Our approach effectively includes short-range exclusion effects and clarifies the clustering behaviors at small scale: PBHs are anti-correlated at short distances.