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

Abstract

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 xH I(z), which is constrained by Lyα forest and damping-wing absorption measurements at z ∼ 5–14, based on ground-based optical and JWST observations. Combining xH I(z) with the Planck CMB power spectra excluding the large-scale E-mode polarization, we obtain τ=0.0552−0.0026+0.0019(stat.)−0.0049+0.0075(sys.) , where the systematic uncertainty accounts for possible absorption-modeling effects in the inference of xH 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–Ωm plane and find a 2.4σ 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, Σmν < 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, Σmν=0.0594−0.0007+0.0113eV . However, the cosmological upper limit and the oscillation-based lower limit show a mild 2.2σ tension, providing an independent indication of possible physics beyond ΛCDM.