Cosmological Constraints from Sunyaev-Zel'dovich-Selected Clusters with X-ray Observations in the First 178 Square Degrees of the South Pole Telescope Survey

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 deg2 of the 2500 deg2 SPT-SZ survey, with 14 clusters having X-ray observations from either Chandra or XMM. Assuming a spatially flat LCDM cosmological model, we find the SPT cluster sample constrain sigma_8 (Omega_m/0.25)^0.30 = 0.785 +- 0.037. In combination with measurements of the CMB power spectrum from the SPT and the seven-year WMAP data, the SPT cluster sample constrain sigma_8 = 0.795 +- 0.016 and Omega_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 LCDM model by including the following as free parameters: the dark energy equation of state (w), the sum of the neutrino masses (sum mnu), the effective number of relativistic species (Neff), and a primordial non-Gaussianity (fNL). We find that adding the SPT cluster data significantly improves the constraints on w and sum mnu 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 sum mnu < 0.28 eV at 95% confidence, a factor of 1.25 and 1.4 improvement, respectively, over the constraints without clusters. [abbrev.]