The clustering evolution of primordial black holes

Primordial black holes might comprise a significant fraction of the dark matter in the Universe and be responsible for the gravitational wave signals from black hole mergers observed by the LIGO/Virgo collaboration. The spatial clustering of primordial black holes might affect their merger rates and have a significant impact on the constraints on their masses and abundances. We provide some analytical treatment of the primordial black hole spatial clustering evolution, compare our results with some of the existing N-body numerical simulations and discuss the implications for the black hole merger rates. If primordial black holes contribute to a small fraction of the dark matter, primordial black hole clustering is not relevant. On the other hand, for a large contribution to the dark matter, we argue that the clustering may increase the late time Universe merger rate to a level compatible with the LIGO/Virgo detection rate. As for the early Universe merger rate of black hole binaries formed at primordial epochs, clustering alleviates the LIGO/Virgo constraints, but does not evade them