Cosmic Cartography: Bayesian reconstruction of the galaxy density informed by large-scale structure

The dark sirens method combines gravitational waves and catalogs of galaxies to constrain the cosmological expansion history, merger rates and mass distributions of compact objects, and the laws of gravity. However, the incompleteness of galaxy catalogs means faint potential host galaxies are unobserved, and must be modeled to avoid inducing a bias. The majority of dark sirens analyses to date assume that the missing galaxies are distributed uniformly across the sky, which is clearly unphysical. We introduce a new Bayesian approach to the reconstruction of galaxy catalogs, which makes full use of our knowledge of large-scale structure. Our method quantifies the uncertainties on the estimated true galaxy number count in each voxel, and is marginalized over cosmological parameters and bias parameters. Crucially, our method further assesses the (absolute) magnitude distribution of galaxies, which is not known from the galaxy catalog itself. We present the details of our method and validate our approach on a galaxy catalog associated to the Millennium Simulation. The tools developed here generate physically-informed and robust host galaxy reconstructions, enabling more informative dark sirens analyses. Stage IV galaxy surveys will display greater redshift overlap with GW observations, whilst remaining incomplete -- emphasizing the importance of our work.