A combined measurement of cosmic growth and expansion from clusters of galaxies, the CMB and galaxy clustering

Combining galaxy cluster data from the ROSAT All-Sky Survey and the Chandra X-ray Observatory, cosmic microwave background (CMB) 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 +/- 0.019 and. = 0.570(-0.063)(+0.064) (at the 68.3 per cent confidence level). Allowing both w and gamma to vary we find w = -0.950(-0.070)(+0.069) and gamma = 0.533 +/- 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 +/- 0.061. For our most general model with a free w, we measure Omega m = 0.278(-0.011)(+0.012), H0 = 70.0 +/- 1.3 km s(-1) Mpc(-1) and w = -0.987(-0.053)(+0.054) for the expansion parameters, and sigma(8) = 0.789 +/- 0.019 and gamma = 0.604 +/- 0.078 for the growth parameters. These results are in excellent agreement with GR+Lambda CDM (gamma similar or equal to 0.55; w = -1) and represent the tightest and most robust simultaneous constraint on cosmic growth and expansion to date.