LIGO/Virgo black holes and dark matter: The effect of spatial clustering
  We discuss the effect of clustering for the determination of the merger rate
of binary black holes in the LIGO mass range. While for a Poissonian initial
distribution, and assuming isolated binaries, the allowed fraction of
Primordial Black Holes (PBHs) to dark matter (DM) is a few percent, we show
that this bound can be relaxed if PBHs are clustered. More precisely we show
that for large clustering the merger rate can drop with increasing fraction of
PBHs, introducing a degeneracy in the parameters of the theory consistent with
a given present merger rate, and allowing all the DM to be in the form of
stellar mass PBHs. This degeneracy can however be broken by looking at the
evolution of the merger rate with redshift. For a simple clustering model that
we consider, we show that the LIGO projected sensitivity can disentangle,
through the observation of a stochastic background of gravitational waves,
different clustered distributions having the same present merger rate.
