This is the third of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive , X-ray flux-selected galaxy clusters .
Our data set consists of 238 clusters drawn from the ROSAT All-Sky Survey , and incorporates extensive follow-up observations using the Chandra X-ray Observatory .
Here we present improved constraints on departures from General Relativity ( GR ) on cosmological scales , using the growth index , \gamma , to parameterize the linear growth rate of cosmic structure .
Using the method of ( ) , we simultaneously and self-consistently model the growth of X-ray luminous clusters and their observable-mass scaling relations , accounting for survey biases , parameter degeneracies and the impact of systematic uncertainties .
Such analysis of the survey and follow-up data is crucial , else spurious constraints may be obtained .
We combine the X-ray cluster growth data with cluster gas mass fraction , type Ia supernova , baryon acoustic oscillation and cosmic microwave background data .
We find that the combination of these data leads to a tight correlation between \gamma and the normalization of the matter power spectrum , \sigma _ { 8 } .
Consistency with GR requires a measured growth index of \gamma \sim 0.55 .
Under the assumption of self-similar evolution and constant scatter in the cluster observable-mass scaling relations , and for a spatially flat model with a cosmological constant , we measure \gamma ( \sigma _ { 8 } / 0.8 ) ^ { 6.8 } = 0.55 ^ { +0.13 } _ { -0.10 } , with allowed values for \sigma _ { 8 } in the range 0.79 to 0.89 ( 68.3 per cent confidence limits ) .
Relaxing the assumptions on the scaling relations by introducing two additional parameters to model possible evolution in the normalization and scatter of the luminosity-mass relation , we obtain consistent constraints on \gamma that are only \sim 20 per cent weaker than those above .
Allowing the dark energy equation of state , w , to take any constant value , we simultaneously constrain the growth and expansion histories , and find no evidence for departures from either GR or the cosmological constant plus cold dark matter paradigm .
Our results represent the most robust consistency test of General Relativity on cosmological scales to date .