  We show that the abundance and redshift distribution ($dN/dz$) of galaxy
clusters in future high--yield cluster surveys, combined with the spatial power
spectrum ($P_c(k)$) of the same clusters, can place significant constraints on
the evolution of the dark energy equation of state, $w=w(a)$. We evaluate the
expected errors on $w_a=-dw/da$ and other cosmological parameters using a
Fisher matrix approach, and simultaneously including cluster structure
evolution parameters in our analysis. We study three different types of
forthcoming surveys that will identify clusters based on their X-ray emission
(such as DUO, the Dark Universe Observatory), their Sunyaev--Zel'dovich (SZ)
decrement (such as SPT, the South Pole Telescope), or their weak lensing (WL)
shear (such as LSST, the Large Synoptic Survey Telescope). We find that
combining the cluster abundance and power spectrum significantly enhances
constraints from either method alone. We show that the weak-lensing survey can
deliver a constraint as tight as $\Delta w_a \sim 0.1$ on the evolution of the
dark energy equation of state, and that the X-ray and SZ surveys each yield
$\Delta w_a \sim 0.4$ separately, or $\Delta w_a \sim 0.2$ when these two
surveys are combined. For the X-ray and SZ surveys, constraints on dark energy
parameters are improved by a factor of two by combining the cluster data with
cosmic microwave background (CMB) anisotropy measurements by Planck, but
degrade by a factor of two if the survey is required to solve simultaneously
for cosmological and cluster structure evolution parameters. The constraint on
$w_a$ from the weak lensing survey is improved by $\sim 25$% with the addition
of Planck data.

Astrophysics