Constraining high-redshift stellar-mass primordial black holes with
  next-generation ground-based gravitational-wave detectors
  The possible existence of primordial black holes in the stellar mass window
has received considerable attention because their mergers may contribute to
current and future gravitational-wave detections. Primordial black hole
mergers, together with mergers of black holes originating from Population~III
stars, are expected to dominate at high redshifts ($z\gtrsim 10$). However the
primordial black hole merger rate density is expected to rise monotonically
with redshift, while Population~III mergers can only occur after the birth of
the first stars. Next-generation gravitational-wave detectors such as Cosmic
Explorer~(CE) and Einstein Telescope~(ET) can access this distinctive feature
in the merger rates as functions of redshift, allowing for a direct measurement
of the abundance of the two populations, and hence for robust constraints on
the abundance of primordial black holes. We simulate four-months worth of data
observed by a CE-ET detector network and perform hierarchical Bayesian analysis
to recover the merger rate densities. We find that if the Universe has no
primordial black holes with masses of $\mathcal{O}(10M_{\odot})$, the projected
upper limit on their abundance $f_{\rm PBH}$ as a fraction of dark matter
energy density may be as low as $f_{\rm PBH}\sim \mathcal{O}({10^{-5}})$, about
two orders of magnitude lower than current upper limits in this mass range. If
instead $f_{\rm PBH}\gtrsim 10^{-4}$, future gravitational wave observations
would exclude $f_{\rm PBH}=0$ at the 95\% credible interval.
