"SNe Ia twins for life" towards a precise determination of H$_{0}$

Abstract

Here we present an approach to the measurement of extragalactic distances using twin SNe Ia, taken from the early down to the nebular phase.The approach is purely empirical, although we can give a theoretical background on why the method is reliable. By studying those twins in galaxies where peculiar velocities are relatively unimportant, we can tackle the H$_{0}$ tension problem. Here we apply the method to the determination of the distances to NGC 7250 and NGC 2525, who hosted respectively SN 2013dy and SN 2018gv, twins of two different SNe Ia prototypes: SN 2013aa/SN 2017cbv and SN2011fe. From the study of the SN 2013aa and SN 2017cbv twin pair, by comparing it with SN 2011fe and applying the difference between the SN 2013aa/2017cbv and the SN 2011fe class, we find as well a good estimate of the distance to NGC 5643. We have just started to measure distances with this method for the samples in Freedman et al. and Riess et al. There are differences in measured distances to the same galaxy using Cepheids or TRGBs. In this context of discrepancy, the ''twins for life '' method is very competitive because it can provide distance estimates with a modulus error of $\sigma_{\mu}$ $=$ 0.04 mag. Our findings called for a revision of the distances measured with Cepheids in Riess et al. (2022). NGC 7250 and NGC 2525 needed better measurements with Cepheids. We have noticed that the Cepheids--based distance obtained with the {\it JWST} in Riess et al. (2024a) for NGC 5643 is in a a good agreement with what we find, unlike their previous estimate in Riess et al. (2022). We address the local SNe Ia distances as part of the Hubble tension problem. We expect to apply the 'twin' SNe Ia comparison from the local sample to galaxies with z $>$0.02--0.03 well into the Hubble flow to obtain a reliable value of H$_{0.}$