No way ou$\tau$: Epoch of Reionization Observations Do not Support Large Values of the Optical Depth to Reionization

Abstract

Recent cosmological analyses combining high-redshift cosmic microwave background (CMB) measurements with low-redshift baryon acoustic oscillation (BAO) data have reported a preference for dynamical dark energy, with the cosmological constant scenario ($\Lambda$CDM) disfavored at the $\sim 3\sigma$ level. These analyses, however, typically rely on large-scale CMB polarization measurements to constrain the optical depth to reionization $\tau_{\rm reio}\sim 0.06$, raising the question of whether potential systematics in this dataset could influence the inferred cosmological preference. Excluding large-scale polarization data substantially weakens the tension with $\Lambda$CDM to the $\lesssim 2\sigma$ level, nevertheless at a price of increasing $\tau_{\rm reio}$ significantly to $\sim 0.09$. Here, we use a physically motivated Gompertzian reionization framework to perform a self-consistent Bayesian analysis combining CMB (excluding large-scale polarization data), BAO, and independent measurements of the neutral hydrogen fraction evolution from quasar damping wing observations and dark pixel constraints. We derive $\tau_{\rm reio} = 0.067 \pm 0.011$ (dynamical dark energy scenario) in good agreement with cosmological analyses that would include large-scale CMB polarization data, while the inferred reionization history is consistent with multiple observational constraints. Our analysis recovers a preference for dynamical dark energy at the $\gtrapprox2\sigma$ level. These results demonstrate that astrophysical probes of reionization independently recover the optical depth required by CMB polarization measurements, suggesting that potential systematics in large-scale polarization alone are unlikely to fully explain the emerging preference for dynamical dark energy.