Projected gravitational wave constraints on primordial black hole abundance for extended mass distributions

We investigate the projected minimum constraints set by next-generation gravitational wave detectors Einstein Telescope and LISA on the abundance of primordial black holes relative to dark matter from both resolvable mergers and the stochastic gravitational wave background (SGWB) for extended primordial black hole mass distributions. We consider broad power law distributions for a range of negative and positive exponents γ and top-hat distributions (with γ = 0) and use the IMRPhenomXAS waveforms to simulate binary sources up to mass ratios qmax = 1000 and redshifts z = 300. Our results suggest that accounting for extended mass distributions have the most apparent impact when considering mergers at high redshifts z > 30, for which the constraint curves have broader mass windows and shift to higher abundances compared to when a monochromatic distribution is assumed; on the other hand, constraints from low-redshift mergers and the SGWB do not change much with the assumed mass distribution. At high redshifts, astrophysical black holes are not expected to contribute significantly, providing possible smoking-gun evidence for PBHs. Constraints derived from LISA and ET observations would complement each other by probing different PBH mass windows and this holds for the extended mass distributions studied.