Self Calibration in Cluster Studies of Dark Energy: Combining the Cluster Redshift Distribution, the Power Spectrum and Mass Measurements

We examine the prospects for measuring the dark energy equation of state parameter w within the context of any uncertain redshift evolution of galaxy cluster structure (building on Majumdar & Mohr 2003) and show that including the redshift averaged cluster power spectrum, (P̄cl), and direct mass measurements of 100 clusters helps tremendously in reducing cosmological parameter uncertainties. Specifically, we show that when combining the redshift distribution and the power spectrum information for a particular X–ray survey (DUET) and two SZE surveys (SPT & Planck), the constraints on the dark energy equation of state w can be improved by roughly a factor of 4. Because surveys designed to study the redshift distribution of clusters will have all the information necessary to construct P̄cl, the benefit of adding P̄cl in reducing uncertainties comes at no additional observational cost. Combining detailed mass studies of 100 clusters with the redshift distribution improves the parameter uncertainties by a factor of 3-5. The data required for these detailed mass measurements– assumed to have 1σ uncertainties of 30%– are accumulating in the the XMM-Newton and Chandra archives. The best constraints are obtained when one combines both the power spectrum constraints and mass measurements with the cluster redshift distribution; when using the survey to extract the parameters and evolution of the mass–observable relations, we estimate the uncertainties on w of ∼4% to 6%. These parameter constraints are obtained from self-calibrating cluster surveys alone. In combination with CMB or distance measurements that have different parameter degeneracies, cluster studies of dark energy will provide enhanced constraints and allow for cross–checks of systematics. Subject headings: cosmic microwave background — galaxies: clusters — cosmology: theory