Clustering effects on the Dark Siren determination of H 0: A simulation study

We investigate the cosmological power of gravitational wave (GWs) events without electromagnetic counterparts using high-resolution, cosmological simulations that include realistic clustering. We assume a near-future detector network (LVK + LIGO India in O5), with sky localisation and distance uncertainty capabilities for binary black holes, of the order of 60 deg. squared and 10% respectively, and with a range of about 1600 Mpc/h. We find that clustering leads to increased convergence of the H0 posteriors, with clear recovery of the input value as early as Ngw = 40 events (a very conservative estimate for O5, which expects thousands of BBHs/year). In contrast, even with Ngw = 100 events in uniform catalogues, the posterior remains largely unconstrained. Additionally, we quantify the role of catalogue completeness and show that levels as low as f = 25% can be competitive with fully complete catalogues, confirming the impact of clustering. Completeness levels of f = 50% perform statistically similar to complete catalogues with as few as Ngw = 40 events. We conclude that improving GWs detection capabilities yields better results than more complete galaxy catalogues.Finally, we find that 1) physical weights do not provide significant additional constraining power on top of clustering, 2) luminosity distance errors contribute more for small cone openings, 3) the H0 prior range does not introduce any biases in the H0 posterior, 4) closer events (≲ 100 Mpc/h) yield about two times better precision than more distant events (≲ 1600 Mpc/h), and 5) our method is robust to different modelling choices.