Dancing in the dark: detecting a population of distant primordial black holes

Primordial black holes (PBHs) are compact objects proposed to have formed in the early Universe from the collapse of small-scale over-densities. Their existence may be detected from the observation of gravitational waves (GWs) emitted by PBH mergers, if the signals can be distinguished from those produced by the merging of astrophysical black holes. In this work, we forecast the capability of the Einstein Telescope, a proposed third-generation GW observatory, to identify and measure the abundance of a subdominant population of distant PBHs, using the difference in the redshift evolution of the merger rate of the two populations as our discriminant. We carefully model the merger rates and generate realistic mock catalogues of the luminosity distances and errors that would be obtained from GW signals observed by the Einstein Telescope. We use two independent statistical methods to analyse the mock data, finding that, with our more powerful, likelihood-based method, PBH abundances as small as $f_\mathrm{PBH} \approx 7 \times 10^{-6}$ ($f_\mathrm{PBH} \approx 2\times10^{-6}$) would be distinguishable from $f_\mathrm{PBH} = 0$ at the level of $3\sigma$ with a one year (ten year) observing run of the Einstein Telescope. Our mock data generation code, darksirens, is fast, easily extendable and publicly available on GitLab.