Dispu$\tau$able: the high cost of a low optical depth

Recent baryonic acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) are mildly discrepant ($2.2\sigma$) with the cosmic microwave background (CMB) when interpreted within $\Lambda$CDM. When analyzing these data with extended cosmologies this inconsistency manifests as a $\simeq3\sigma$ preference for sub-minimal neutrino mass or evolving dark energy. It is known that the preference for sub-minimal neutrino mass from the suppression of structure growth could be alleviated by increasing the optical depth to reionization $\tau$. We show that, because the CMB-inferred $\tau$ is negatively correlated with the matter fraction, a larger optical depth resolves a similar preference from geometric constraints. Optical depths large enough to resolve the neutrino mass tension ($\tau\sim0.09)$ reduce the preference for evolving dark energy from $\simeq3\sigma$ to $\simeq1.5\sigma$ and increase the CMB-inferred values of $n_s$ and $H_0$ to $0.968\pm0.004$ and $67.94\pm0.44$ km/s/Mpc, respectively. Conversely, within $\Lambda$CDM the combination of DESI BAO, high-$\ell$ CMB and CMB lensing yields $\tau = 0.090 \pm 0.012$, which is in $\simeq3-5\sigma$ tension with Planck low-$\ell$ polarization data when taken at face value. Essentially all current CMB analyses $-$ including recent results from WMAP+ACT and SPT $-$ adopt the Planck measurement of $\tau$: thus a systematic in large-scale Planck polarization would serve as a "single-point failure" for most modern cosmological analyses that include CMB data. While there is no evidence for systematics in the large-scale Planck data, $\tau$ remains the least well-constrained $\Lambda$CDM parameter and is far from its cosmic variance limit. This strengthens the case for future large-scale CMB experiments as well as direct probes of the epoch of reionization.