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

TL;DR

This study derives a CMB optical depth constraint ($τ$) independent of the Planck large-scale E-mode polarization by reconstructing the reionization history from $x_{HI}(z)$ measurements (Ly$\alpha$ forest, damping wings, and JWST data) and combining with CMB power spectra that exclude low-$l$ polarization. A Gaussian process regression yields a smooth, monotonic $x_{HI}(z)$, enabling a precise $τ$ estimate of $0.0552^{+0.0019}_{-0.0026}$ (stat) and $0.0552^{+0.0075}_{-0.0049}$ (systematics), broadly consistent with Planck results that include lowE. The joint analysis tightens constraints on $A_s$, $n_s$, and $S_8$, and reveals a $2.4\sigma$ tension with DESI DR2 BAO in the $H_0 r_d$–$Ω_m$ plane, hinting at physics beyond $Λ$CDM. When $Σm_ν$ is allowed to vary, the study finds $Σm_ν<0.0550$ eV (95%), favoring normal ordering, with a mild $2.2σ$ tension against oscillation-based lower bounds, suggesting possible new physics in cosmology or particle physics.

Abstract

Recent studies report a mild discrepancy between baryon acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements within the $Λ$CDM 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 $x_\mathrm{HI}(z)$, which is constrained by Lyman-$α$ 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 $τ=0.0552^{+0.0019}_{-0.0026}$, a stringent constraint consistent with the previous CMB results including the large-scale E-mode. We also evaluate a potential systematic error in our method associated with absorption modeling, obtaining $τ=0.0552^{+0.0075}_{-0.0049}$. Using this constraint on $τ$, we resolve the degeneracy in the $τ$-$Ω_m$ plane and find a $2.4σ$ tension with the DESI DR2 BAO results, thereby confirming the claimed mild discrepancy suggestive of physics beyond $Λ$CDM. Finally, we derive an upper limit on the sum of neutrino masses, $Σm_ν<0.0550\,(0.0717)$ 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, $Σm_ν=0.0594_{-0.0007}^{+0.0113}$ eV. 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 $Λ$CDM.

Figures (9)

• Figure 1: Cosmic reionization history reconstructed via Gaussian process regression. The black line represents the median reionization history, while the gray shaded regions show the 68% (dark gray) and 95% (light gray) posterior ranges. We also present $x_\mathrm{H\,\textsc{i}}$ estimates based on various methods used in this work: Ly$\alpha$ damping-wing absorption of GRBs (blue squares; totani06totani14fausey25), QSOs (orange circles; greig22durovcikova24), LBGs (green diamonds; umeda25b), LAE clustering (purple pentagons; umeda25a), Ly$\alpha$ luminosity function (cyan pluses; wold22umeda25a), Ly$\alpha$ EW distribution (pink stars; mason19ajung20whitler20bolan22kageura25), and Ly$\alpha$/$\beta$ forests (olive crosses; zhu22davies25). The brown dotted lines indicate the redshift corresponding to instantaneous reionization with $\tau=0.09$ and $\tau=0.0552$, for $\Omega_bh^2=0.02237$, $\Omega_ch^2=0.1200$, and $h=0.6736$. We note that the instantaneous reionization redshift $z=7.73$ for $\tau=0.0552$ differs from the midpoint of reionization $z_\mathrm{mid}=7.19$, since the actual reionization history is not instantaneous.
• Figure 2: Constraints on cosmological parameters and $\tau$ for the $\Lambda$CDM model. The orange contours represent constraints derived from CMB Planck TTTEEE and Planck+ACT lensing and cosmic reionization history, excluding low-$l$ EE. The blue and black contours indicate constraints obtained from CMB (w/o lowE) and CMB (w/ lowE), respectively. The dark and light contours show the 68% and 95% regions, respectively.
• Figure 3: Comparison of our $\tau$ values with those from previous studies. The orange circles show our $\tau$ values from CMB (w/o lowE) and CMB (w/o lowE)+$x_\mathrm{H\,\textsc{i}}(z)$. The purple and blue points indicate $\tau$ values from WMAP wmap03wmap12 and Planck planck13_16planck15_13planck18_6, respectively. The cyan circles show results from ACT act25 and SPT spt25 combined with Planck data. The green circles represent $\tau$ constraints from elbers25 based on reionization history, BAO, and BBN, and from garciagallego25 based on the Ly$\alpha$ forest.
• Figure 4: Constraints on $H_0$ and $\Omega_m$ for the $\Lambda$CDM model. The blue, black, and orange contours show results based on CMB (w/o lowE), CMB (w/ lowE), and CMB (w/o lowE)+$x_\mathrm{H\,\textsc{i}}(z)$, respectively. The green region for $\Omega_m$ indicates constraints from DESI DR2 BAO measurements, while the green region for $H_0$ shows results from DESI DR2 BAO data with a BBN prior on $\omega_b$. Contours show the 68% and 95% regions.
• Figure 5: Constraints on $H_0r_d$ and $\Omega_m$ for the $\Lambda$CDM model from DESI DR2 BAO (green), CMB (w/o lowE) (blue), and CMB (w/o lowE)+$x_\mathrm{H\,\textsc{i}}(z)$ (orange). The result including reionization history in this work is consistent with the CMB (w/ lowE) constraint and is in $2.4\sigma$ tension with the DESI DR2 BAO measurements. Contours show the 68% and 95% regions.