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 our earlier work) and show that including the redshift-averaged cluster power spectrum ((P) over bar (cl)) 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 Sunyaev-Zel'dovich effect surveys (South Pole Telescope and 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 (P) over bar cl, the benefit of adding (P) over bar (cl) 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 1 sigma uncertainties of 30%-are accumulating in the XMM-Newton and Chandra archives. The best constraints are obtained when one combines both the power spectrum constraints and the mass measurements with the cluster redshift distribution; when using the survey to extract the parameters and evolution of the mass-observable relations, we estimate uncertainties on w of similar to4%-6%. These parameter constraints are possible with cluster surveys that are carried out over large, contiguous regions of the sky, so that the cluster power spectrum can be reasonably measured. In combination with cosmic microwave background or distance measurements that have different parameter degeneracies, cluster studies of dark energy will provide enhanced constraints and allow for cross-checks of systematics.