The Pantheon+ Analysis: Evaluating Peculiar Velocity Corrections in Cosmological Analyses with Nearby Type Ia Supernovae

Separating the components of redshift due to expansion and motion in the nearby universe ($z<0.1$) is critical for using Type Ia Supernovae (SNe Ia) to measure the Hubble constant ($H_0$) and the equation-of-state parameter of dark energy ($w$). Here, we study the two dominant 'motions' contributing to nearby peculiar redshifts: large-scale, coherent-flow (CF) motions and small-scale motions due to gravitationally-associated galaxies deemed to be in a galaxy group. We use a set of 585 low-$z$ SNe from the Pantheon+ sample, and evaluate the efficacy of corrections to these motions by measuring the improvement of SN distance residuals. We study multiple methods for modeling the large and small-scale motions and show that while group assignments and CF corrections individually contribute to small improvements in Hubble residual scatter, the greatest improvement comes from the combination of the two (relative standard deviation of the Hubble residuals RSD improves from 0.167 mag to 0.157 mag). We find the optimal flow corrections derived from various local density maps significantly reduce Hubble residuals while raising $H_0$ by $\sim0.4$ km s$^{-1}$ Mpc$^{-1}$ as compared to using CMB redshifts, disfavoring the hypothesis that unrecognized local structure could resolve the Hubble tension. We estimate that the systematic uncertainties in cosmological parameters after optimally correcting redshifts are 0.08-0.17 km s$^{-1}$ Mpc$^{-1}$ in $H_0$ and 0.02-0.03 in $w$ which are smaller than the statistical uncertainties for these measurements: 1.5 km s$^{-1}$ Mpc$^{-1}$ for $H_0$ and 0.04 for $w$.