Mitigating the optical depth degeneracy using the kinematic Sunyaev-Zel'dovich effect with CMB-S4

The epoch of reionization is one of the major phase transitions in the history of the universe, and is a focus of ongoing and upcoming cosmic microwave background (CMB) experiments with improved sensitivity to small-scale fluctuations. Reionization also represents a significant contaminant to CMB-derived cosmological parameter constraints, due to the degeneracy between the Thomson-scattering optical depth, $\tau$, and the amplitude of scalar perturbations, $A_s$. This degeneracy subsequently hinders the ability of large-scale structure data to constrain the sum of the neutrino masses, a major target for cosmology in the 2020s. In this work, we explore the kinematic Sunyaev-Zel'dovich (kSZ) effect as a probe of reionization, and show that it can be used to mitigate the optical depth degeneracy with high-sensitivity, high-resolution data from the upcoming CMB-S4 experiment. We discuss the dependence of the kSZ power spectrum on physical reionization model parameters, as well as on empirical reionization parameters, namely $\tau$ and the duration of reionization, $\Delta z$. We show that by combining the kSZ two-point function and the reconstructed kSZ four-point function, degeneracies between $\tau$ and $\Delta z$ can be strongly broken, yielding tight constraints on both parameters. We forecast $\sigma(\tau) = 0.003$ and $\sigma(\Delta z) = 0.25$ for a combination of CMB-S4 and Planck data, including detailed treatment of foregrounds and atmospheric noise. The constraint on $\tau$ is nearly identical to the cosmic-variance limit that can be achieved from large-angle CMB polarization data. The kSZ effect thus promises to yield not only detailed information about the reionization epoch, but also to enable high-precision cosmological constraints on the neutrino mass.