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 stateparameter w within the context of any uncertain redshift evolution of galaxycluster structure (building on Majumdar and Mohr, 2003) and show that includingthe redshift averaged cluster power spectrum, P_cl(k), and direct massmeasurements of 100 clusters helps tremendously in reducing cosmologicalparameter uncertainties. Specifically, we show that when combining the redshiftdistribution and the power spectrum information for a particular X-ray survey(DUET) and two SZE surveys (SPT & Planck), the constraints on the dark energyequation of state w can be improved by roughly a factor of 4. Because surveysdesigned to study the redshift distribution of clusters will have all theinformation necessary to construct P_cl(k), the benefit of adding P_cl(k) inreducing uncertainties comes at no additional observational cost. Combiningdetailed mass studies of 100 clusters with the redshift distribution improvesthe parameter uncertainties by a factor of 3-5. The data required for thesedetailed mass measurements-- assumed to have 1sigma uncertainties of 30-- areaccumulating in the the XMM-Newton and Chandra archives. The best constraintsare obtained when one combines both the power spectrum constraints and massmeasurements with the cluster redshift distribution; when using the survey toextract the parameters and evolution of the mass--observable relations, weestimate the uncertainties on w of ~4% to 6%. These parameter constraints areobtained from self-calibrating cluster surveys alone. In combination with CMBor distance measurements that have different parameter degeneracies, clusterstudies of dark energy will provide enhanced constraints and allow forcross--checks of systematics.Comment: 9 pages, 4 figures, submitted to Ap