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

We present constraints on the mean matter density, Ω_m, dark energy density, Ω_DE, and the dark energy equation of state parameter, w, using Chandra measurements of the X-ray gas mass fraction (f_gas) in 42 hot (kT > 5keV), X-ray luminous, dynamically relaxed galaxy clusters spanning the redshift range 0.05 < z < 1.1. Using only the f_gas data for the six lowest redshift clusters at z < 0.15, for which dark energy has a negligible effect on the measurements, we measure Ω_m = 0.28 +/- 0.06 (68 per cent confidence limits, using standard priors on the Hubble constant, H₀, and mean baryon density, Ω_bh²). Analysing the data for all 42 clusters, employing only weak priors on H₀ and Ω_bh², we obtain a similar result on Ω_m and a detection of the effects of dark energy on the distances to the clusters at ~99.99 per cent confidence, with Ω_DE = 0.86 +/- 0.21 for a non-flat ΛCDM model. The detection of dark energy is comparable in significance to recent type Ia supernovae (SNIa) studies and represents strong, independent evidence for cosmic acceleration. Systematic scatter remains undetected in the f_gas data, despite a weighted mean statistical scatter in the distance measurements of only ~5 per cent. For a flat cosmology with a constant dark energy equation of state, we measure Ω_m = 0.28 +/- 0.06 and w = -1.14 +/- 0.31. Combining the f_gas data with independent constraints from cosmic microwave background and SNIa studies removes the need for priors on Ω_bh² and H₀ and leads to tighter constraints: Ω_m = 0.253 +/- 0.021 and w = -0.98 +/- 0.07 for the same constant-w model. Our most general analysis allows the equation of state to evolve with redshift. Marginalizing over possible transition redshifts 0.05 < z_t < 1, the combined f_gas + CMB + SNIa data set constrains the dark energy equation of state at late and early times to be w₀ = -1.05 +/- 0.29 and w_et = -0.83 +/- 0.46, respectively, in agreement with the cosmological constant paradigm. Relaxing the assumption of flatness weakens the constraints on the equation of state by only a factor of ~2. Our analysis includes conservative allowances for systematic uncertainties associated with instrument calibration, cluster physics and data modelling. The measured small systematic scatter, tight constraint on Ω_m and powerful constraints on dark energy from the f_gas data bode well for future dark energy studies using the next generation of powerful X-ray observatories, such as Constellation-X.