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 w 0 , the early‐time equation of state w et , and the scalefactor at transition a t . From a combined analysis of all three data sets, assuming a constant equation of state and that the Universe is flat, we measure w 0 =−1.05 +0.10 −0.12 . Including w et as a free parameter and allowing the transition scalefactor to vary over the range 0.5 < a t < 0.95 where the data sets have discriminating power, we measure w 0 =−1.27 +0.33 −0.39 and w et =−0.66 +0.44 −0.62 . 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 Ω m and alleviates a number of other parameter degeneracies, including that between the scalar spectral index n s , the physical baryon density Ω b h 2 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 w 0 =−1.09 +0.12 −0.15 and obtain a tight constraint on the current dark energy density Ω 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 c 2 s = 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 w et , which would be tighter than those mentioned above by approximately a factor of 2 with the current data.