Constraining Dark Energy with X-ray Galaxy Clusters, Supernovae and the Cosmic Microwave Background

We present new constraints on the evolution of dark energy from an analysis of Cosmic Microwave Background, supernova and X-ray galaxy cluster data. Our analysis employs a minimum of priors and exploits the complementary nature of these data sets. We examine a series of dark energy models with up to three free parameters: the current dark energy equation of state w0, the early time equation of state wet and the scale factor at transition, at. From a combined analysis of all three data sets, assuming a constant equation of state and that the Universe is flat, we measure w0 = 1.05-0.12+0.10. Including wet as a free parameter and allowing the transition scale factor to vary over the range 0.5 < at < 0.95 where the data sets have discriminating power, we measure w0 = -1.27-0.39+0.33 and wet = -0.66-0.62+0.44. We find no significant evidence for evolution in the dark energy equation of state parameter with redshift. Marginal hints of evolution in the supernovae data become less significant when the cluster constraints are also included in the analysis. The complementary nature of the data sets leads to a tight constraint on the mean matter density, (Omega)m and alleviates a number of other parameter degeneracies, including that between the scalar spectral index ns, the physical baryon density (Omega)bh2 and the optical depth τ. This complementary nature also allows us to examine models in which we drop the prior on the curvature. For non-flat models with a constant equation of state, we measure w0 = -1.09-0.15+0.12 and obtain a tight constraint on the current dark energy density, (Omega)de = 0.70 ± 0.03. For dark energy models other than a cosmological constant, energy-momentum conservation requires the inclusion of spatial perturbations in the dark energy component. Our analysis includes such perturbations, assuming a sound speed cs2 = 1 in the dark energy fluid as expected for Quintessence scenarios. For our most general dark energy model, not including such perturbations would lead to spurious constraints on wet which would be tighter than those mentioned above by approximately a factor two with the current data