Union3.1: Reducing Systematics in Supernova Cosmology with Self-consistent Measurements of Host Galaxy Properties for 2000 Type Ia Supernovae

Photometrically derived distances of Type Ia supernovae (SNe Ia) rely on a $\sim5\%$ empirical correction based on host galaxy properties, e.g., global stellar mass. Unbiased cosmology inference therefore requires the self-consistent determination of host properties across the full range of redshifts probed, which we undertake here for approximately 2000 SNe in the Union3 compilation (now Union3.1). We use homogeneous, optical-infrared photometry from the DESI Legacy Imaging Surveys to infer global galaxy properties using the stellar population synthesis and SED-fitting code Prospector. We find that the host masses of $z