Reconstructing cosmic growth with kinetic Sunyaev-Zel’dovich observations in the era of stage IV experiments

Future ground-based cosmic microwave background (CMB) experiments will generate competitive large-scale structure data sets by precisely characterizing CMB secondary anisotropies over a large fraction of the sky. We describe a method for constraining the growth rate of structure to sub-1% precision out to $z\ensuremath{\approx}1$, using a combination of galaxy cluster peculiar velocities measured using the kinetic Sunyaev-Zel'dovich (kSZ) effect, and the velocity field reconstructed from galaxy redshift surveys. We consider only thermal SZ-selected cluster samples, which will consist of $\mathcal{O}(1{0}^{4}--1{0}^{5})$ sources for Stage 3 and 4 CMB experiments respectively. Three different methods for separating the kSZ effect from the primary CMB are compared, including a novel blind ``constrained realization'' method that improves signal-to-noise by a factor of $\ensuremath{\sim}2$ over a commonly-used aperture photometry technique. Assuming a correlation between the integrated tSZ $y$-parameter and the cluster optical depth, it should then be possible to break the kSZ velocity-optical depth degeneracy. The effects of including CMB polarization and SZ profile uncertainties are also considered. In the absence of systematics, a combination of future Stage 4 experiments should be able to measure the product of the growth and expansion rates, $\ensuremath{\alpha}\ensuremath{\equiv}fH$, to better than 1% in bins of $\mathrm{\ensuremath{\Delta}}z=0.1$ out to $z\ensuremath{\approx}1$---competitive with contemporary redshift-space distortion constraints from galaxy surveys. We conclude with a discussion of the likely impact of various systematics.