Combining galaxy cluster data from the ROSAT All-Sky Survey and the Chandra X-ray Observatory , cosmic microwave background data from the Wilkinson Microwave Anisotropy Probe , and galaxy clustering data from the WiggleZ Dark Energy Survey , the 6-degree Field Galaxy Survey and the Sloan Digital Sky Survey III , we test for consistency the cosmic growth of structure predicted by General Relativity ( GR ) and the cosmic expansion history predicted by the cosmological constant plus cold dark matter paradigm ( \Lambda CDM ) .
The combination of these three independent , well studied measurements of the evolution of the mean energy density and its fluctuations is able to break strong degeneracies between model parameters .
We model the key properties of cosmic growth with the normalization of the matter power spectrum , \sigma _ { 8 } , and the cosmic growth index , \gamma , and those of cosmic expansion with the mean matter density , \Omega _ { m } , the Hubble constant , H _ { 0 } , and a kinematical parameter equivalent to that for the dark energy equation of state , w .
For a spatially flat geometry , w = -1 , and allowing for systematic uncertainties , we obtain \sigma _ { 8 } = 0.785 \pm 0.019 and \gamma = 0.570 ^ { +0.064 } _ { -0.063 } ( at the 68.3 per cent confidence level ) .
Allowing both w and \gamma to vary we find w = -0.950 ^ { +0.069 } _ { -0.070 } and \gamma = 0.533 \pm 0.080 .
To further tighten the constraints on the expansion parameters , we also include supernova , Cepheid variable and baryon acoustic oscillation data .
For w = -1 , we have \gamma = 0.616 \pm 0.061 .
For our most general model with a free w , we measure \Omega _ { m } = 0.278 ^ { +0.012 } _ { -0.011 } , H _ { 0 } = 70.0 \pm 1.3 ~ { } { km } \allowbreak { } ~ { } { s } ^ { -1 } \allowbreak { } { Mpc } % ^ { -1 } and w = -0.987 ^ { +0.054 } _ { -0.053 } for the expansion parameters , and \sigma _ { 8 } = 0.789 \pm 0.019 and \gamma = 0.604 \pm 0.078 for the growth parameters .
These results are in excellent agreement with GR+ \Lambda CDM ( \gamma \simeq 0.55 ; w = -1 ) and represent the tightest and most robust simultaneous constraint on cosmic growth and expansion to date .