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, ${\tau }_{\mathrm{reion}}$. Next, we carry out a Markov chain Monte Carlo (MCMC) analysis based on the Pantheon+sh0es type Ia supernova sample to infer the best-fit values of the model parameters, and then use these to evaluate ${\tau }_{\mathrm{reion}}$. We obtain ${\tau }_{\mathrm{reion}}=0.0581_{-0.0096}^{+0.0105}$ (68% confidence limits). This result indicates that, when Pantheon+sh0es data are used to constrain the model parameters, our backreaction model yields a value of ${\tau }_{\mathrm{reion}}$ 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 nonstandard physics.

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• Cosmological parameters
• Evolution of the Universe
• Large scale structure of the Universe
• Distances, redshifts, & velocities