# Clustering of primordial black holes with non-Gaussian initial fluctuations

## TL;DR

This paper investigates how primordial black hole clustering depends on the nature of initial fluctuations, showing Gaussian fluctuations do not induce clustering on large scales, but non-Gaussianity can enhance it.

## Contribution

It formulates the two-point correlation function of PBHs at formation using a functional integration approach, highlighting the impact of non-Gaussianity on clustering.

## Key findings

- Gaussian fluctuations do not induce super-Hubble scale clustering.
- Non-Gaussianity via local-type trispectrum enhances PBH clustering.
- Clustering is sensitive to the primordial curvature perturbation statistics.

## Abstract

We formulate the two-point correlation function of primordial black holes (PBHs) at their formation time, based on the functional integration approach which has often been used in the context of halo clustering. We find that PBH clustering on super-Hubble scales could never be induced in the case where the initial primordial fluctuations are Gaussian, while it can be enhanced by the so-called local-type trispectrum (four-point correlation function) of the primordial curvature perturbations.