Recovering Large-Scale Clustering of Missing Galaxies for Galaxy--Gravitational-Wave Cross-correlations
We present a framework for completing galaxy catalogs from flux-limited surveys which reconstructs the missing galaxy population while preserving its clustering properties. This is particularly important for cosmological analyses using gravitational-wave (GW) dark sirens without electromagnetic counterparts, such as binary black hole mergers, which constitute the majority of GW detections. As GW detectors probe increasingly larger distances, galaxy catalogs become progressively incomplete owing to survey flux limits. Current state-of-the-art statistical host identification methods typically account for this incompleteness by assuming that the missing galaxies are uniformly distributed in comoving volume. While this approximation can mitigate biases due to incompleteness, it neglects the clustering of galaxies within the cosmic web. Since galaxies and GW sources are both expected to trace the underlying large-scale structure, their spatial distributions are correlated, making a homogeneous reconstruction physically unrealistic, a shortcoming which our framework addresses. As a proof of concept, we apply the method to simulated galaxy catalogs with different flux limits and observational selection functions. Our approach provides a significantly more realistic completion of incomplete galaxy catalogs than the commonly adopted homogeneous-in-comoving-volume approximation, enabling more robust cosmological inference from gravitational-wave dark sirens.