| Summary: | We use measurements from the South Pole Telescope (SPT) Sunyaev-Zel'dovich (SZ) cluster survey in combination with X-ray measurements to constrain cosmological parameters. We present a statistical method that fits for the scaling relations of the SZ and X-ray cluster observables with mass while jointly fitting for cosmology. The method is generalizable to multiple cluster observables, and self-consistently accounts for the effects of the cluster selection and uncertainties in cluster mass calibration on the derived cosmological constraints. We apply this method to a data set consisting of an SZ-selected catalog of 18 galaxy clusters at z > 0.3 from the first 178 deg[superscript 2] of the 2500 deg[superscript 2] SPT-SZ survey, with 14 clusters having X-ray observations from either Chandra or XMM-Newton. Assuming a spatially flat ΛCDM cosmological model, we find the SPT cluster sample constrains σ[subscript 8](Ω [subscript m] /0.25)[superscript 0.30] = 0.785 ± 0.037. In combination with measurements of the cosmic microwave background (CMB) power spectrum from the SPT and the seven-year Wilkinson Microwave Anisotropy Probe data, the SPT cluster sample constrains σ[subscript 8] = 0.795 ± 0.016 and Ω [subscript m] = 0.255 ± 0.016, a factor of 1.5 improvement on each parameter over the CMB data alone. We consider several extensions beyond the ΛCDM model by including the following as free parameters: the dark energy equation of state (w), the sum of the neutrino masses (Σm [subscript ν]), the effective number of relativistic species (N [subscript eff]), and a primordial non-Gaussianity (f [subscript NL]). We find that adding the SPT cluster data significantly improves the constraints on w and Σm [subscript ν] beyond those found when using measurements of the CMB, supernovae, baryon acoustic oscillations, and the Hubble constant. Considering each extension independently, we best constrain w = –0.973 ± 0.063 and the sum of neutrino masses Σm [subscript ν] < 0.28 eV at 95% confidence, a factor of 1.25 and 1.4 ...
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