A New Constraint on the Optical Depth from the Reionization History Independent of Cosmic Microwave Background Large-scale E-mode Polarization

Recent studies report a mild discrepancy between baryon acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements within the ΛCDM framework. This discrepancy could be explained if the optical depth τ inferred from the CMB large-scale E-mode polarization is underestimated, which may be biased by foreground-subtraction or instrumental systematics. In this work, we present a determination of τ independent of the large-scale E-mode polarization, using the latest measurements of the redshift evolution of the neutral hydrogen fraction x H I ( z ), which is constrained by Ly α forest and damping-wing absorption measurements at z ∼ 5–14, based on ground-based optical and JWST observations. Combining x H I ( z ) with the Planck CMB power spectra excluding the large-scale E-mode polarization, we obtain τ = 0.055 2 − 0.0026 + 0.0019 ( stat. ) − 0.0049 + 0.0075 ( sys. ) , where the systematic uncertainty accounts for possible absorption-modeling effects in the inference of x H I ( z ). This constraint is consistent with previous CMB results including the large-scale E-mode polarization. With this measurement, we resolve the degeneracy in the τ –Ω m plane and find a 2.4 σ tension with the DESI DR2 BAO results, thereby confirming the claimed mild discrepancy suggestive of physics beyond ΛCDM. Finally, we derive an upper limit on the sum of neutrino masses, Σ m ν < 0.0550 (0.0717) eV, at the 95% (99%) confidence level. This limit favors the normal mass ordering and, when combined with the lower limits from neutrino oscillation experiments, yields a further constraint, Σ m ν = 0.059 4 − 0.0007 + 0.0113 eV . However, the cosmological upper limit and the oscillation-based lower limit show a mild 2.2 σ tension, providing an independent indication of possible physics beyond ΛCDM.