Leveraging SN Ia spectroscopic similarity to improve the measurement of $H_0$

Recent studies suggest spectroscopic differences explain a fraction of the variation in Type Ia supernova (SN Ia) luminosities after light-curve/color standardization. In this work, (i) we empirically characterize the variations of standardized SN Ia luminosities, and (ii) we use a spectroscopically inferred parameter, SIP, to improve the precision of SNe Ia along the distance ladder and the determination of the Hubble constant ($H_0$). First, we show that the \texttt{Pantheon+} covariance model modestly overestimates the uncertainty of standardized magnitudes by $\sim 7$%, in the parameter space used by the $\texttt{SH0ES}$ Team to measure $H_0$; accounting for this alone yields $H_0 = 73.01 \pm 0.92$ km s$^{-1}$ Mpc$^{-1}$. Furthermore, accounting for spectroscopic similarity between SNe~Ia on the distance ladder reduces their relative scatter to $\sim0.12$ mag per object (compared to $\sim 0.14$ mag previously). Combining these two findings in the model of SN covariance, we find an overall 14% reduction (to $\pm 0.85$km s$^{-1}$ Mpc$^{-1}$) of the uncertainty in the Hubble constant and a modest increase in its value. Including a budget for systematic uncertainties itemized by Riess et al. (2022a), we report an updated local Hubble constant with $\sim1.2$% uncertainty, $H_0 = 73.29 \pm 0.90$km s$^{-1}$ Mpc$^{-1}$. We conclude that spectroscopic differences among photometrically standardized SNe Ia do not explain the ``Hubble tension." Rather, accounting for such differences increases its significance, as the discrepancy against $\Lambda$CDM calibrated by the ${\it Planck}$ 2018 measurement rises to 5.7$\sigma$.