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  • Letter
  • Open Access

Constraints on the Thomson optical depth to the Cosmic Microwave Background from the Lyman-α forest

Olga Garcia-Gallego1,2,*, Vid Iršič2,3,†, Martin G. Haehnelt1,2, and James S. Bolton4

  • 1Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
  • 2KICC—Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
  • 3Center for Astrophysics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield AL10 9AB, United Kingdom
  • 4School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

  • *Contact author: og313@cam.ac.uk
  • †Contact author: v.irsic@herts.ac.uk
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Phys. Rev. Research 8, L032009 – Published 20 July, 2026

DOI: https://doi.org/10.1103/4hgw-9cqg

Abstract

We present the first constraints on the electron optical depth to reionization, τe, from the Lyman-α forest alone for physically motivated reionization models that match the reionization's end point, zend, required by the same astrophysical probe, and for symmetric reionization models with fixed duration, Δz, commonly adopted in cosmic microwave background (CMB) reionization analyses. Compared to traditional estimates from the latter, the Lyman-α forest traces the ionization state of the Intergalactic medium (IGM) through its coupling with the thermal state. We find an explicit mapping between the two by solving the chemistry and temperature evolution equations for hydrogen and helium. Our results yield τe = 0.040−0.018+0.042 (95% C.L.) and τe = 0.041−0.017+0.028 for reionization models with zend and Δz fixed, respectively. With mock Lyman-α forest data that mimics the precision of future larger quasar sample datasets, we would potentially obtain tighter τe constraints, paving the way for CMB-independent constraints on the epoch of reionization from a large-scale structure probe.

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Phys. Rev. Research 8, L032009– Published 20 July, 2026
  • Received 4 October 2025
  • Revised 4 February 2026
  • Accepted 11 May 2026
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