The Pantheon+ Analysis: Improving the Redshifts and Peculiar Velocities
  of Type Ia Supernovae Used in Cosmological Analyses
  We examine the redshifts of a comprehensive set of published Type Ia
supernovae, and provide a combined, improved catalog with updated redshifts. We
improve on the original catalogs by using the most up-to-date heliocentric
redshift data available; ensuring all redshifts have uncertainty estimates;
using the exact formulae to convert heliocentric redshifts into the Cosmic
Microwave Background (CMB) frame; and utilizing an improved peculiar velocity
model that calculates local motions in redshift-space and more realistically
accounts for the external bulk flow at high-redshifts. In total we reviewed
2821 supernova redshifts; 534 are comprised of repeat-observations of the same
supernovae and 1764 pass the cosmology sample quality cuts. We found 5 cases of
missing or incorrect heliocentric corrections, 44 incorrect or missing
supernova coordinates, 230 missing heliocentric or CMB frame redshifts, and
1200 missing redshift uncertainties. Of the 2287 unique Type Ia supernovae in
our sample (1594 of which satisfy cosmology-sample cuts) we updated 990
heliocentric redshifts. The absolute corrections range between $10^{-8} \leq
\Delta z \leq 0.038$, and RMS$(\Delta z) \sim 3\times 10^{-3}$. The sign of the
correction was essentially random, so the mean and median corrections are
small: $4\times 10^{-4}$ and $4\times 10^{-6}$ respectively. We examine the
impact of these improvements for $H_0$ and the dark energy equation of state
$w$ and find that the cosmological results change by $\Delta H_0 = -0.11$ km
s$^{-1}$ Mpc$^{-1}$ and $\Delta w = -0.001$, both significantly smaller than
previously reported uncertainties for $H_0$ of 1.4 km s$^{-1}$ Mpc$^{-1}$ and
$w$ of 0.04 respectively.
