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 ( f _ { gas } ) in 42 hot ( kT > 5 keV ) , 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 \Omega _ { m } = 0.28 \pm 0.06 ( 68 per cent confidence limits , using standard priors on the Hubble Constant , H _ { 0 } , and mean baryon density , \Omega _ { b } h ^ { 2 } ) .
Analyzing the data for all 42 clusters , employing only weak priors on H _ { 0 } and \Omega _ { b } h ^ { 2 } , we obtain a similar result on \Omega _ { m } and a detection of the effects of dark energy on the distances to the clusters at \sim 99.99 per cent confidence , with \Omega _ { DE } = 0.86 \pm 0.21 for a non-flat \Lambda CDM 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 \sim 5 per cent .
For a flat cosmology with a constant dark energy equation of state , we measure \Omega _ { m } = 0.28 \pm 0.06 and w = -1.14 \pm 0.31 .
Combining the f _ { gas } data with independent constraints from cosmic microwave background and SNIa studies removes the need for priors on \Omega _ { b } h ^ { 2 } and H _ { 0 } and leads to tighter constraints : \Omega _ { m } = 0.253 \pm 0.021 and w = -0.98 \pm 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 w _ { 0 } = -1.05 \pm 0.29 and w _ { et } = -0.83 \pm 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 \sim 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 \Omega _ { 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 .