Signatures of primordial black holes in gravitational wave clustering

The possible existence of primordial black holes (PBHs) is an open question in modern cosmology. Among the probes to test it, gravitational waves (GW) coming from their mergers constitute a powerful tool. In this work, we study how stellar mass PBH binaries could affect measurements of the clustering of merger events in future GW surveys. We account for PBH binaries formed both in the early and late Universe and show that the power spectrum modification they introduce can be detected at $\sim 2\sigma-3\sigma$ (depending on some assumptions) whenever PBH mergers make up at least $\sim 60\%$ of the overall number of detected events. By adding cross-correlations with galaxy surveys, this threshold is lowered to $\sim 40\%$. In the case of a poor redshift determination of GW sources, constraints are degraded by about a factor of 2. Assuming a theoretical model for the PBH merger rate, we can convert our results to constraints on the fraction of dark matter in PBHs, $f_{\rm PBH}$. Finally, we perform a Bayesian model selection forecast and confirm that the analysis we develop could be able to detect $\sim30M_\odot$ PBHs if they account for $f_{\rm PBH}\sim 10^{-4}-10^{-3}$, depending on the model uncertainty considered, being thus competitive with other probes.