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arXiv · 2402.00600

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

Pierre Auclair·Baptiste Blachier
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Abstract

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. Using a scale-independent collapse threshold, we derive explicit expressions for the excess probability to find pairs of PBHs separated by a distance $r$, as well as the excess probability to find pairs with asymmetric mass ratio. Our framework is model-independent by construction and we discuss possible other applications.

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Pierre Auclair, Baptiste Blachier. 2024-02-01. Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects. https://doi.org/10.1103/physrevd.109.123538

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