Merger History of Clustered Primordial Black Holes

Primordial black hole (PBH) binaries experience strong gravitational perturbations in the case of their initial clustering, which significantly affects the dynamics of their mergers. In this work, we develop a new formalism to account for these perturbations and track the evolution of the binary orbital parameters distribution. Based on this approach, we calculate the merger rate of PBH binaries and demonstrate that its temporal evolution differs greatly from that of isolated binary systems. Moreover, PBH clustering produces distinctive features in the stochastic gravitational-wave background: the canonical $2\mathrm{/}3$ spectral slope transforms to ${\mathrm{\Omega }}_{\mathrm{g}\mathrm{w}}\propto {\nu }^{-65\mathrm{/}28}$ in a certain frequency band. These predictions can be probed in future gravitational wave observations, opening up new opportunities to test the clustering of PBHs and their contribution to dark matter.