Breaking Cosmological Degeneracies in Galaxy Cluster Surveys with a Physical Model of Cluster Structure

It has been shown that in an idealized galaxy cluster survey, containing >~10,000 clusters, statistical errors on dark energy and other cosmological parameters would be at the percent level. Furthermore, through ``self-calibration,'' parameters describing the mass-observable relation and cosmology could be simultaneously determined, although at a loss in accuracy by about an order of magnitude. Here we examine an alternative approach to self-calibration, in which a parameterized ab initio physical model is used to compute theoretical mass-observable relations from the cluster structure. As an example, we use a modified-entropy (``preheating'') model of the intracluster medium, with the history and magnitude of entropy injection as unknown input parameters. Using a Fisher matrix approach, we evaluate the expected simultaneous statistical errors on cosmological and cluster model parameters. We find that compared to a phenomenological parameterization of the mass-observable relation, our physical model yields significantly tighter constraints in both surveys and offers substantially improved synergy when the two surveys are combined. In a mock X-ray survey, we find statistical errors on the dark energy equation of state are a factor of 2 tighter than the phenomenological model, with Δw₀~0.08 and its evolution, Δw_a≡-Δdw/da~0.23, with corresponding errors of Δw₀~0.06 and Δw_a~0.17 from a mock Sunyaev-Zel'dovich (SZ) survey, both with N_cl~2.2×10⁴ clusters, while simultaneously constraining cluster model parameters to <~10%. When the two surveys are combined, the constraints tighten to Δw₀~0.03 and Δw_a~0.1, a 40% improvement over adding the individual experiment errors in quadrature and a factor of 2 improvement over the phenomenological model. This suggests that parameterized physical models of cluster structure would be useful when extracting cosmological constraints from SZ and X-ray cluster surveys.