The clustering of dark sirens' invisible host galaxies

Dark sirens are a powerful way to infer cosmological and astrophysical parameters from the combination of gravitational wave sirens and galaxy catalogues. Importantly, the method relies on the completeness of the galaxy catalogues being well modelled. A magnitude-limited catalogue will always be incomplete to some extent, requiring a completion scheme to avoid biasing the parameter inference. Standard methods include homogeneous and multiplicative completion, which have the advantage of simplicity but underestimate or overestimate the amplitude of structure at low completeness, respectively. In this work, we propose a new method to complete galaxy catalogues which uses clustering information to incorporate knowledge of the large scale structure into the dark sirens method. We find that if the structure of the true number of galaxies is sufficiently well preserved in the catalogue, our estimator can perform drastically better than both homogeneous and multiplicative completion. We lay the foundations for a maximally informative dark sirens analysis and discuss its limitations.