Turning a negative neutrino mass into a positive optical depth

Under $\mathrm{\ensuremath{\Lambda}}$ cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$), recent baryon acoustic oscillation (BAO) distance measures from DESI, which favor a low matter density ${\mathrm{\ensuremath{\Omega}}}_{m}$, are in moderate $2--3\ensuremath{\sigma}$ tension with cosmic microwave background (CMB) observations. This tension appears alternately as a preference for the sum of neutrino masses dropping below the $\ensuremath{\sum}{m}_{\ensuremath{\nu}}=0.06\text{ }\text{ }\mathrm{eV}$ value required by neutrino oscillation measurements to formally negative values; a discrepant value of ${\mathrm{\ensuremath{\Omega}}}_{m}$ at 0.06 eV; or preference for dynamical dark energy beyond $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. We show that this tension largely arises from the CMB lensing constraints on the calibration of the sound horizon for geometric measurements and relies on the measurement of the reionization optical depth $\ensuremath{\tau}$ from large-angle CMB polarization to set the lensing amplitude. Dropping these constraints removes the neutrino tension at $\ensuremath{\sum}{m}_{\ensuremath{\nu}}=0.06\text{ }\text{ }\mathrm{eV}$ entirely, favoring $\ensuremath{\tau}=0.091\ifmmode\pm\else\textpm\fi{}0.011$ in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. Beyond $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, it brings the preference for ${w}_{0}\ensuremath{-}{w}_{a}$ dynamical dark energy to below 95% CL. We explore the freedom in interpreting the low-$\ensuremath{\ell}$ EE polarization constraint due to analysis choices and reionization modeling beyond the standard step-function assumption and find that this drops the neutrino tension in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ to below 95% CL. Alternately, this raising of $\ensuremath{\tau}$ can also be achieved by the same reduction in large-scale curvature fluctuations that also ameliorates the low-$\ensuremath{\ell}$ temperature anomaly.