Comments on the Union3 "Spline-Interpolated Distance Moduli" Model

Abstract: The Union3 "Spline-Interpolated Distance Moduli" model posterior has been distributed for third-party cosmology analysis. The posterior prefers a large value of $\Omega_M$, a small absolute value of $w_0$, and a negative $w_a$, but still accommodates $\Lambda$CDM; the supernova data alone are not strongly constraining. The posterior is built assuming an underlying model and prior, both of which must be made to conform with any new model and prior being analyzed. The posterior is calculated for a prior that is not flat but rather has non-trivial structure in $\Omega_M$-$w_0$-$w_a$; the associated likelihood is slightly shifted relative to the posterior. The posterior for a prior that is flat in $\Omega_M$-$w_0$-$w_a$ is also shifted relative to the original, but not at a level that is statistically significant. The misapplication of Union3 results in the "DESI2024 VI" cosmology fits are inconsequential.