Optical depth to reionization in a Universe with multiple inhomogeneous domains

We study the optical depth to reionization in a cosmological setting that includes backreaction from matter inhomogeneities, using the Buchert averaging formalism. We construct a spacetime model consisting of multiple inhomogeneous domains, hereafter referred to as the backreaction model, characterized by a set of parameters. We first examine how these parameters influence the computation of the optical depth to reionization, $\tau_{reion}$. Next, we carry out a Markov Chain Monte Carlo (MCMC) analysis based on the PantheonPlus+SH0ES Type Ia supernova sample to infer the best-fit values of the model parameters, and then use these to evaluate $\tau_{reion}$. We obtain $\tau_{reion} = 0.0581^{+0.0105}_{-0.0096}$ (68$\%$ confidence limits). This result indicates that, when PantheonPlus+SH0ES data are used to constrain the model parameters, our backreaction model yields a value of $\tau_{reion}$ that aligns more closely with observational estimates than the value predicted by the standard cosmological model. We further demonstrate that the backreaction model leads to a modest reduction of the Hubble tension, while avoiding the need for exotic or non-standard physics.