| Summary: | 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 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 all three surveys can deliver a constraint as tight as Delta(w_a) ~ 0.3 on the evolution of the dark energy equation of state. 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. For the weak lensing survey, constraints are improved by a factor of six by combining it with Planck data.
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