Constraining the Evolution of Dark Energy with a Combination of Galaxy   Cluster Observables
  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. 
Sheng Wang (Columbia, Brookhaven), Justin Khoury (Columbia), Zoltan   Haiman (Columbia) and Morgan May (Brookhaven)