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 $f_{\mathrm{P}\mathrm{B}\mathrm{H}}$ as a fraction of dark matter energy density may be as low as $f_{\mathrm{P}\mathrm{B}\mathrm{H}}\sim \mathcal{O}({10}^{-5})$, about two orders of magnitude lower than current upper limits in this mass range. If instead $f_{\mathrm{P}\mathrm{B}\mathrm{H}}\gtrsim {10}^{-4}$, future gravitational wave observations would exclude $f_{\mathrm{P}\mathrm{B}\mathrm{H}}=0$ at the 95% credible interval.