Does Dark Siren Cosmology Depend on the Host Galaxies of the Merger Event?

Dark siren cosmology is made possible by LIGO measured distances and spatial localizations and astronomer measured galaxy catalogs with redshifts or photometric redshifts. A central question is what if the binary black hole (BBH) mergers occur in galaxies not in the galaxy catalog? For example what if BBH mergers occur in low metallicity dwarf galaxies and we are using a highly complete massive red galaxy catalog? In cosmology this question is stated as: what if the galaxy tracer population has a bias relative to the dark matter different than the BBH mergers do? Does the H0 measurement made by a using a statistical redshift from galaxy photometric redshift catalogs and LIGO luminosity distances and spatial localizations depend on the bias of the source population and the bias of the tracer population? As different galaxy catalogs have different bias relative to dark matter. we use fast lognormal galaxy distributions generated by FLASK from matter-matter power spectra to simulate galaxy catalogs with different bias. We use these catalogs to measure the H₀ measurement bias as a function of the source and tracer population bias.