Hubble tension and small-scale inhomogeneities on light propagation

Context. A major observational challenge within the standard cosmological framework is the Hubble tension, a statistically significant ($\sim 5\sigma$) disagreement between the Hubble constant derived from cosmic microwave background measurements and the value obtained through local distance-ladder methods based on Type Ia supernovae and Cepheid variable stars. Aims. 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. Methods. We employ two distinct formulations of the ZKDR equation to test our hypothesis using recent Type Ia supernovae datafrom the Pantheon+ compilation and the SH0ES collaboration and six gravitational lens systems from the H0LiCOW collaboration. Results. We obtained constraints on the cosmological parameters and the ZKDR model parameters within the framework of the inhomogeneous models considered. The model comparison criterion indicates that the data show weak preference of $\Lambda$CDM over the flat ZKDR model , whereas the remaining models studied are strongly disfavored. Conclusions. Our findings indicate that a background model characterized by the ZKDR approximation and its modifications does not solve or alleviate the Hubble tension.