Clustering of primordial black holes formed in a matter-dominated epoch

TL;DR

This paper derives a general formula for primordial black hole clustering considering primordial non-Gaussianity, compares clustering in matter- and radiation-dominated epochs, and discusses observational constraints.

Contribution

It introduces a new formula for PBH clustering without high-peak approximation and applies it to matter-dominated epoch formation scenarios.

Findings

Clustering is less significant in matter-dominated epoch than in radiation-dominated epoch.

PBH clustering exceeds Poisson shot noise in many cases.

Relations to CMB isocurvature constraints are quantitatively analyzed.

Abstract

In the presence of the local-type primordial non-Gaussianity, it is known that the clustering of primordial black holes (PBHs) emerges even on super-horizon scales at the formation time. This effect has been investigated in the high-peak limit of the PBH formation in the radiation-dominated epoch in the literature. There is another possibility that the PBH formation takes place in the early matter-dominated epoch. In this scenario, the high-peak limit is not applicable because even initially small perturbations grow and can become a PBH. We first derive a general formula to estimate the clustering of PBHs with primordial non-Gaussianity without assuming the high-peak limit, and then apply this formula to a model of PBH formation in a matter-dominated epoch. Clustering is less significant in the case of the PBH formation in the matter-dominated epoch than that in the radiation-dominated epoch. Nevertheless, it is much larger than the Poisson shot noise in many cases. Relations to the constraints of the isocurvature perturbations by the cosmic microwave background radiation are quantitatively discussed.