A New Constraint on the Optical Depth from the Reionization History Independent of CMB Large-Scale E-Mode Polarization

Abstract

Recent studies report a mild discrepancy between BAO and CMB measurements within the $\Lambda$CDM framework. This discrepancy could be explained if the optical depth $\tau$ 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 $\tau$ independent of the large-scale E-mode polarization, using the latest measurements of the redshift evolution of the neutral hydrogen fraction $x_\mathrm{HI}(z)$, which is constrained by Lyman-$\alpha$ forest and damping-wing absorption measurements at $z\sim5$--$14$, based on ground-based optical and JWST observations. Combining $x_\mathrm{HI}(z)$ with the Planck CMB power spectra excluding the large-scale E-mode polarization, we obtain $\tau=0.0552^{+0.0019}_{-0.0026}(\mathrm{stat.})^{+0.0075}_{-0.0049}(\mathrm{sys.})$, where the systematic uncertainty accounts for possible absorption-modeling effects in the inference of $x_\mathrm{HI}(z)$. This constraint is consistent with previous CMB results including the large-scale E-mode polarization. With this measurement, we resolve the degeneracy in the $\tau$--$\Omega_{\rm m}$ plane and find a $2.4\sigma$ tension with the DESI DR2 BAO results, thereby confirming the claimed mild discrepancy suggestive of physics beyond $\Lambda$CDM. Finally, we derive an upper limit on the sum of neutrino masses, $\Sigma m_\nu < 0.0550\,(0.0717)\,{\rm eV}$ 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, $\Sigma m_\nu = 0.0594_{-0.0007}^{+0.0113}\,{\rm eV}$. However, the cosmological upper limit and the oscillation-based lower limit show a mild $2.2\sigma$ tension, providing an independent indication of possible physics beyond $\Lambda$CDM.