Complementing the ground-based CMB Stage-4 experiment on large scales with the PIXIE satellite

We present forecasts for cosmological parameters from future Cosmic Microwave Background (CMB) data measured by the Stage-4 (S4) generation of ground-based experiments in combination with large-scale anisotropy data from the PIXIE satellite. We demonstrate the complementarity of the two experiments and focus on science targets that benefit from their combination. We show that a cosmic-variance-limited measurement of the optical depth to reionization provided by PIXIE, with error $\sigma(\tau)=0.002$, is vital for enabling a 5$\sigma$ detection of the sum of the neutrino masses when combined with a CMB-S4 lensing measurement, and with lower-redshift constraints on the growth of structure and the distance-redshift relation. Parameters characterizing the epoch of reionization will also be tightly constrained; PIXIE's $\tau$ constraint converts into $\sigma(\rm{z_{re}})=0.2$ for the mean time of reionization, and a kinematic Sunyaev-Zel'dovich measurement from S4 gives $\sigma(\Delta \rm{z_{re}})=0.03$ for the duration of reionization. Both PIXIE and S4 will put strong constraints on primordial tensor fluctuations, vital for testing early-universe models, and will do so at distinct angular scales. We forecast $\sigma(r)\approx 5\times10^{-4}$ for a signal with a tensor-to-scalar ratio $r=10^{-3}$, after accounting for diffuse foreground removal and de-lensing. The wide and dense frequency coverage of PIXIE results in an expected foreground-degradation factor on $r$ of only $\approx$25%. By measuring large and small scales PIXIE and S4 will together better limit the energy injection at recombination from dark matter annihilation, with $p_{\rm ann}<0.09 \times 10^{-6} \ {\rm m^3/s/Kg}$ projected at 95% confidence. Cosmological parameters measured from the damping tail with S4 will be best constrained by polarization, which has the advantage of minimal contamination from extragalactic emission.