Gaussian Process Reconstruction of Galaxy Catalogs Tightens Dark Siren H0 Constraints by up to 66% in Mocks

The arXiv preprint from Matteo Tagliazucchi introduces a hierarchical Bayesian scheme that treats the redshift distribution along each GW line of sight as a draw from a Gaussian process conditioned on the observed incomplete catalog and the survey selection function. This replaces the standard assumption that missing galaxies are uniformly distributed in comoving volume, thereby retaining clustering information that directly informs the luminosity-distance–redshift relation used to constrain H0.

Standard dark-siren analyses lose precision when catalogs are sparse because they discard the very over- and under-densities that anchor individual events to specific host redshifts. The GP approach recovers these features non-parametrically, producing the largest gains (66%) precisely in sightlines where homogeneous filling erases the strongest clustering signals. The improvement scales inversely with catalog completeness, indicating the method is most valuable for current and near-future surveys whose spectroscopic coverage remains patchy.

Context from LIGO-Virgo-KAGRA O4 and DESI data releases shows that the dominant systematic in present H0 inferences is indeed catalog incompleteness rather than waveform modeling. By propagating selection-function uncertainty through the GP, the new framework also supplies a principled route to marginalize over that systematic, something earlier catalog-based analyses handled only approximately.

The main limitation is reliance on mock catalogs; real-data tests with O5 events and next-generation spectroscopic surveys will be required to confirm that GP hyperparameters remain stable when selection functions are imperfectly known.