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

Abstract

Gravitational waves (GWs) offer an alternative way to measure the Hubble parameter. The
optimal technique, the “bright siren” approach, requires the identification of an electromagnetic counterpart. However, a significant fraction of gravitational waves signals will not have
counterparts. Such events can still constrain the Hubble parameter ????0 via statistical methods,
exploiting galaxy information from the GWs sky localisation volume. In this work, we investigate the power of this method using high-resolution, cosmological simulations that include
realistic clustering. We find that clustering leads to increased convergence of the ????0 posteriors, with clear recovery of the input value as early as ????gw = 40 events, compared to uniform
catalogues, where the posterior remains largely unconstrained, even with ????gw = 100 events.
In addition, we quantify the role of catalogue incompleteness. We show that catalogues
with completeness levels as low as ???? = 25% can be competitive with fully complete catalogues,
confirming the impact of clustering. Completeness levels of ???? = 50% perform statistically
similar to complete catalogues with as few as ????gw = 40 events. This indicates the need to focus
on improving gravitational waves detection capabilities, rather than obtaining more complete
galaxy catalogues.
Finally, we investigate additional properties of the method by taking into consideration
physical weights, different observational errors, potential biases from the ????0 priors, a variety
of detectors’ horizon distances, and different methods of catalogue completion and statistical
analysis.