Improved constraints on dark energy from Chandra X-ray observations of the largest relaxed galaxy clusters

We present constraints on the mean matter density, Omega_m, dark energy density, Omega_de, and the dark energy equation of state parameter, w, using Chandra measurements of the X-ray gas mass fraction (fgas) in 42 hot (kT>5keV), X-ray luminous, dynamically relaxed galaxy clusters spanning the redshift range 0.05<z<1.1. Using only the fgas data for the 6 lowest redshift clusters at z<0.15, for which dark energy has a negligible effect on the measurements, we measure Omega_m=0.28+-0.06 (68% confidence, using standard priors on the Hubble Constant, H_0, and mean baryon density, Omega_bh^2). Analyzing the data for all 42 clusters, employing only weak priors on H_0 and Omega_bh^2, we obtain a similar result on Omega_m and detect the effects of dark energy on the distances to the clusters at ~99.99% confidence, with Omega_de=0.86+-0.21 for a non-flat LCDM model. The detection of dark energy is comparable in significance to recent SNIa studies and represents strong, independent evidence for cosmic acceleration. Systematic scatter remains undetected in the fgas data, despite a weighted mean statistical scatter in the distance measurements of only ~5%. For a flat cosmology with constant w, we measure Omega_m=0.28+-0.06 and w=-1.14+-0.31. Combining the fgas data with independent constraints from CMB and SNIa studies removes the need for priors on Omega_bh^2 and H_0 and leads to tighter constraints: Omega_m=0.253+-0.021 and w=-0.98+-0.07 for the same constant-w model. More general analyses in which we relax the assumption of flatness and/or allow evolution in w remain consistent with the cosmological constant paradigm. Our analysis includes conservative allowances for systematic uncertainties. The small systematic scatter and tight constraints bode well for future dark energy studies using the fgas method. (Abridged)