Union3.1: Self-consistent Measurements of Host Galaxy Properties for 2000 Type Ia Supernovae

The determination of distances using time-series photometry of Type Ia supernovae (SNe Ia) relies on a ~5% empirical correction related to the properties of their host galaxies, e.g., global stellar mass. It is therefore crucial for unbiased cosmology inference that host galaxy properties be self-consistently determined across the full range of redshifts probed, which we undertake in this study for approximately 2000 SNe in the Union3 compilation (now Union3.1). We use aperture-matched, homogeneously-reduced, optical-infrared photometry from the DESI Legacy Imaging Surveys to derive global galaxy properties using the stellar population synthesis and SED-fitting code Prospector. We find that the host masses of $z<0.10$ SNe in Union3 were, on average, overestimated relative to the rest of the sample, 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. We then update the UNITY SN analysis and find that the uncertainties on all standardization parameters shrink to 0.6-0.9x their previous sizes. For flat-$\Lambda$CDM, we find $\Omega_m=0.344^{+0.026}_{-0.025}$, a -0.3$\sigma$ shift from Union3. We then combine with measurements of Baryon Acoustic Oscillations (BAO) and the Cosmic Microwave Background (CMB) exactly as done by DESI DR2 and find $w_0=-0.719\pm0.084$, $w_a=-0.95^{+0.29}_{-0.26}$, corresponding to 3.4$\sigma$ evidence against a cosmological constant (down from 3.8$\sigma$). We also update the DESI combined probe analysis using our correction to Pantheon+ and the recent DES-SN5YR Dovekie recalibration, finding $3.2\sigma$ (up from 2.8$\sigma$) and 3.4$\sigma$ (down from 4.2$\sigma$) evidence against a cosmological constant in the $w_0w_a$ plane, altogether marking a significantly improved consistency across SN analyses.