Enhancing dark siren cosmology via Gaussian process reconstruction of incomplete galaxy catalogs

Abstract

We present a novel framework for improving dark siren cosmology by applying a Gaussian process (GP) to the line-of-sight (LOS) reconstruction of incomplete galaxy catalogs. In the standard galaxy catalog method for inferring the Hubble constant $H_0$ from gravitational-wave (GW) dark sirens, missing galaxies are typically assumed to follow a uniform distribution in comoving volume, an assumption that discards galaxy redshift clustering information crucial for cosmological inference. We propose instead to model the LOS galaxy redshift distribution as a non-parametric function drawn from a GP realization, which is fitted to the observed incomplete catalog via a hierarchical Bayesian likelihood that explicitly accounts for the survey selection function. Applied to mock GW and galaxy catalogs extending up to redshift $z\leq0.4$, our method yields $H_0$ constraints that are on average 23% more precise than the standard homogeneous completion when using a 24%-complete galaxy catalog, and 37% more precise for an 8%-complete catalog. The largest improvement, reaching 66%, is obtained in configurations where the GP most effectively reconstructs the redshift over- and under-density features that the homogeneous completion fails to capture.