We present constraints on the mean matter density , \Omega _ { \mathrm { m } } , the normalization of the density fluctuation power spectrum , \sigma _ { 8 } , and the dark-energy equation-of-state parameter , w , obtained from measurements of the X-ray luminosity function of the largest known galaxy clusters at redshifts z < 0.7 , as compiled in the Massive Cluster Survey ( MACS ) and the local BCS and REFLEX galaxy cluster samples .
Our analysis employs an observed mass–luminosity relation , calibrated by hydrodynamical simulations , including corrections for non-thermal pressure support and accounting for the presence of intrinsic scatter .
Conservative allowances for all known systematic uncertainties are included , as are standard priors on the Hubble constant and mean baryon density .
We find \Omega _ { \mathrm { m } } = 0.28 ^ { +0.11 } _ { -0.07 } and \sigma _ { 8 } = 0.78 ^ { +0.11 } _ { -0.13 } for a spatially flat , cosmological-constant model , and \Omega _ { \mathrm { m } } = 0.24 ^ { +0.15 } _ { -0.07 } , \sigma _ { 8 } = 0.85 ^ { +0.13 } _ { -0.20 } and w = -1.4 ^ { +0.4 } _ { -0.7 } for a flat , constant- w model ( marginalized 68 per cent confidence intervals ) .
Our findings constitute the first determination of the dark-energy equation of state from measurements of the growth of cosmic structure in galaxy clusters , and the consistency of our result with w = -1 lends additional support to the cosmological-constant model .
Future work improving our understanding of redshift evolution and observational biases affecting the mass–X-ray luminosity relation have the potential to significantly tighten these constraints .
Our results are consistent with those from recent analyses of type Ia supernovae , cosmic microwave background anisotropies , the X-ray gas mass fraction of relaxed galaxy clusters , baryon acoustic oscillations and cosmic shear .
Combining the new X-ray luminosity function data with current supernova , cosmic microwave background and cluster gas fraction data yields the improved constraints \Omega _ { \mathrm { m } } = 0.269 \pm 0.016 , \sigma _ { 8 } = 0.82 \pm 0.03 and w = -1.02 \pm 0.06 .