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 about5% 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<0.1 SNe in Union3 were on average overestimated, while the opposite was true for z<0.15 SNe in Pantheon+. After correction, the two studies' average distance modulus estimated for low-redshift SNe, previously >0.03 mag discrepant, come into 0.01 mag agreement. Updating the UNITY SN analysis, we find the uncertainties on all standardization parameters shrink to 0.6 - 0.9 times their previous sizes. For flat- Λ CDM, we find from SNe alone Ω m=0.344+0.026-0.025 (a-0.4σ shift from Union3). We then combine with measurements of Baryon Acoustic Oscillations and the Cosmic Microwave Background exactly as done by DESI DR2 and find for flat w 0w a CDM, w 0=-0.719 plus or minus0.084 and w a=-0.95+0.29-0.26, corresponding to 3.4σ evidence against a cosmological constant (down from 3.8σ per DESI-DR2+Planck+Union3). Updating the DESI-DR2+Planck+SN combined probe analysis with the recent Dovekie recalibration of DES-SN5YR (B. Popovic et al. 2025) or the updated Pantheon+, we find 3.4σ (was 4.2σ before Dovekie) and 3.2σ (was 2.8σ before our correction to Pantheon+) evidence, respectively, against a cosmological constant--a significantly improved consistency between SN analyses.