Hubble tension and small-scale inhomogeneities on light propagation

Abstract: One of the observational challenges in the standard cosmological model is known as the Hubble tension. This $\sim$ 5$\sigma$ discrepancy between early and late measurements of the Hubble Constant arises from observations that rely on cosmological distance estimates, either explicitly or implicitly. In this study, we relax the assumption of the Friedmann-Lema^itre-Robertson-Walker (FLRW) distance-redshift relation and explore the influence of small-scale inhomogeneities on the propagation of light from distant sources, using the Zeldovich-Kantowski-Dyer-Roeder (ZKDR) approximation as an alternative approach to address this tension. We employ the ZKDR equation along with a modified version to test our hypothesis using recent Type Ia supernovae data from the Pantheon+ compilation and the SH0ES collaboration and six gravitational lens systems from the H0LiCOW collaboration. Our findings indicate that a background model characterized by the ZKDR approximation and its modifications does not solve or alleviate the Hubble tension.