Spatial clustering of primordial black holes

The possibility that primordial black holes are the dark matter (or a fraction thereof) has attracted much attention recently. Their spatial clustering is a fundamental property which determines, among others, whether current observational constraints are evaded within a given mass range, whether merging is significant and whether primordial black holes could generate cosmological structure. We treat them as discrete objects and clarify the issue of their spatial clustering, with an emphasis on short-range exclusion and its impact on their large-scale power spectrum. Even if a Poissonian self-pair term is always present in the zero-lag correlation, this does not necessarily imply that primordial black holes are initially Poisson distributed. However, while the initial PBH clustering depends on the detailed shape of the small-scale power spectrum, we argue that it is not relevant for a narrow spectral feature and primordial black hole masses still allowed by observations.