Constraining Dark Energy by Combining Cluster Counts and Shear-Shear Correlations in a Weak Lensing Survey

We study the potential of a large future weak-lensing survey to constrain dark energy properties by using both the number counts of detected galaxy clusters (sensitive primarily to density fluctuations on small scales) and tomographic shear-shear correlations (restricted to large scales). We use the Fisher matrix formalism, assume a flat universe and parameterize the equation of state of dark energy by w(a)=w_0+w_a(1-a), to forecast the expected statistical errors from either observable, and from their combination. We show that the covariance between these two observables is small, and argue that therefore they can be regarded as independent constraints. We find that when the number counts and the shear-shear correlations (on angular scales l < 1000) are combined, an LSST (Large Synoptic Survey Telescope)-like survey can yield statistical errors on (Omega_DE, w_0, w_a) as tight as (0.003, 0.03, 0.1). These values are a factor of 2-25 better than using either observable alone. The results are also about a factor of two better than those from combining number counts of galaxy clusters and their power spectrum.