Primordial black holes with mass ratio-modulated initial clustering: Merger suppression and projected constraints

We present a modification of the expected local primordial black hole (PBH) count $N(y)$, typically seen in the context of the early PBH binary merger rate as a term in the merger rate suppression. We utilize recent results in small-scale PBH clustering to formulate $N(y)$ in such a way that accounts for variations in the binary mass ratio $q$. We then examine how this change affects the projected constraints on PBH abundance from simulated Einstein Telescope (ET) and LISA mergers. Our results indicate that for broadly extended mass distributions, the merger suppression is greatly reduced for binaries with $q\ensuremath{\gg}1$. This leads to an enhanced merger rate for binary distributions favoring a lighter average mass. This change is best reflected by an extension of the low mass end of the constraint windows derived from the resolvable merger channel, although this result is present as well in the stochastic gravitational wave background (SGWB) constraints. Our results imply that the assumption of PBH clustering is testable at abundances and mass ranges much lower than anticipated. Note however that we have only considered the two-body merger channel in this work; a more thorough analysis of our scenario will require a study on the dynamics involved in the three-body merger channel for broad mass distributions, which we leave to future work.