New Constraints on Dark Energy from the Observed Growth of the Most X-ray Luminous Galaxy Clusters

We present constraints on the mean matter density, (Omega)m, normalization of the density fluctuation power spectrum, σ8, and dark energy equation of state parameter, w, obtained from the X-ray luminosity function of the Massive Cluster Survey (MACS) in combination with the local BCS and REFLEX galaxy cluster samples. Our analysis incorporates the mass function predictions of Jenkins et al. (2001), a mass-luminosity relation calibrated using the data of Reiprich and Bohringer (2002), and standard priors on the Hubble constant, H0, and mean baryon density, (Omega)b h2. We find (Omega)m=0.27 +0.06-0.05 and σ8=0.77 +0.07-0.06 for a spatially flat, cosmological constant model, and (Omega)m=0.28 +0.08-0.06, σ8=0.75 ± 0.08 and w=-0.97 +0.20-0.19 for a flat, constant-w model. Our findings constitute the first precise determination of the dark energy equation of state from measurements of the growth of cosmic structure in galaxy clusters. The consistency of our result with w=-1 lends strong additional support to the cosmological constant model. The constraints are insensitive to uncertainties at the 10-20 percent level in the mass function and in the redshift evolution o the mass-luminosity relation; the constraint on dark energy is additionally robust against our choice of priors and known X-ray observational biases affecting the mass-luminosity relation. Our results compare favorably with those from recent analyses of type Ia supernovae, cosmic microwave background anisotropies, the X-ray gas mass fraction of relaxed galaxy clusters and cosmic shear. A simplified combination of the luminosity function data with supernova, cosmic microwave background and cluster gas fraction data using importance sampling yields the improved constraints (Omega)m=0.263 ± 0.014, σ8=0.79 ± 0.02 and w=-1.00 +- 0.05