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.]
