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Optical depth to reionization in a universe with multiple inhomogeneous domains

Shashank Shekhar Pandey1,*, Ruchika2,3,4,†, Subhadeep Mukherjee1,‡, and A. S. Majumdar1,§

  • *Contact author: shashankpandey7347@gmail.com
  • †Contact author: ruchika.science@usal.es
  • ‡Contact author: shubhadeep.avg@gmail.com
  • §Contact author: archan@bose.res.in
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Phys. Rev. D 114, 043552 – Published 26 August, 2026

DOI: https://doi.org/10.1103/dgly-z27m

Abstract

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, τreion. 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 τreion. We obtain τreion=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 τreion 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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Phys. Rev. D 114, 043552– Published 26 August, 2026
  • Received 26 April 2026
  • Accepted 30 July 2026
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