Reconstructing cosmic growth with kSZ observations in the era of Stage
  IV experiments
  Future ground-based CMB experiments will generate competitive large-scale
structure datasets 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 $z\approx 1$, 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 $\mathcal{O}(10^4-10^5)$ 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 $\sim 2$ over
a commonly-used aperture photometry technique. Measurements of the integrated
tSZ $y$-parameter are used to break the kSZ velocity-optical depth degeneracy,
and the effects of including CMB polarization and SZ profile uncertainties are
also considered. A combination of future Stage 4 experiments should be able to
measure the product of the growth and expansion rates, $\alpha\equiv f H$, to
better than 1% in bins of $\Delta z = 0.1$ out to $z \approx 1$ -- competitive
with contemporary redshift-space distortion constraints from galaxy surveys.
