Merger rates in primordial black hole clusters without initial binaries
  Primordial black holes formed through the collapse of cosmological density
fluctuations have been hypothesised as contributors to the dark matter content
of the Universe. At the same time, their mergers could contribute to the
recently observed population of gravitational-wave sources. We investigate the
scenario in which primordial black holes form binaries at late times in the
Universe. Specifically, we re-examine the mergers of primordial black holes in
small clusters of ~30 objects in the absence of initial binaries. Binaries form
dynamically through Newtonian gravitational interactions. These binaries act as
heat sources for the cluster, increasing the cluster's velocity dispersion,
which inhibits direct mergers through gravitational-wave two-body captures.
Meanwhile, three-body encounters of tight binaries are too rare to tighten
binaries sufficiently to allow them to merge through gravitational-wave
emission. We conclude that in the absence of initial binaries, merger rates of
primordial black holes in the Bird et al. (2016) initial cluster configuration
are at least an order of magnitude lower than previously suggested, which makes
gravitational-wave detections of such sources improbable.
