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Clustering of Primordial Black Holes: Basic Results

Authors: James R. Chisholm

Comments: 22 pages, 3 figures; submitted to PRD

We investigate the spatial clustering properties of primordial black holes (PBHs). With minimal assumptions, we show that PBHs are created highly clustered. They constitute an isocurvature perturbation that is non-linear upon horizon entry. Using the peaks theory model of bias, we compute the PBH two-point correlation function and power spectrum. A consequence of this is that PBHs cannot serve as the majority of dark matter in the universe. We show that this clustering could lead to PBH mergers that spoil the mass-creation time relation.