Mitigating the optical depth degeneracy in the cosmological measurement of neutrino masses using 21-cm observations

Massive neutrinos modify the expansion history of the universe and suppress the structure formation below their free streaming scale. Cosmic microwave background (CMB) observations at small angular scales can be used to constrain the total mass $\Sigma m_\nu$ of the three neutrino flavors. However, at these scales, the CMB-measured $\Sigma m_\nu$ is degenerate with $\tau$, the optical depth to reionization, which quantifies the damping of CMB anisotropies due to the scattering of CMB photons with free electrons along the line of sight. Here we revisit the idea to use 21-cm power spectrum observations to provide direct estimates for $\tau$. A joint analysis of CMB and 21-cm data can alleviate the $\tau-\Sigma m_\nu$ degeneracy, making it possible to measure $\Sigma m_\nu$ with unprecedented precision. Forecasting for the upcoming Hydrogen Epoch of Reionization Array (HERA), we find that a $\lesssim\mathcal{O}(10\%)$ measurement of $\tau$ is achievable, which would enable a $\gtrsim 5\sigma$ measurement of $\Sigma m_\nu=60\,[{\rm meV}]$, for any astrophysics model that we considered. Precise estimates of $\tau$ also help reduce uncertainties in other cosmological parameters, such as $A_s$, the amplitude of the primordial scalar fluctuations power spectrum.