We present a velocity-dispersion-based mass calibration of the South Pole Telescope Sunyaev-Zel'dovich effect survey (SPT-SZ) galaxy cluster sample. Using a homogeneously selected sample of 100 cluster candidates from 720 deg2 of the survey along with 63 velocity dispersion (? v ) and 16 X-ray Y X measurements of sample clusters, we simultaneously calibrate the mass-observable relation and constrain cosmological parameters. Our method accounts for cluster selection, cosmological sensitivity, and uncertainties in the mass calibrators. The calibrations using ? v and Y X are consistent at the 0.6? level, with the ? v calibration preferring ~16% higher masses. We use the full SPTCL data set (SZ clusters ? v Y X) to measure ?8(?m/0.27)0.3 = 0.809 ± 0.036 within a flat ?CDM model. The SPT cluster abundance is lower than preferred by either the WMAP9 or Planck WMAP9 polarization (WP) data, but assuming that the sum of the neutrino masses is ?m ? = 0.06 eV, we find the data sets to be consistent at the 1.0? level for WMAP9 and 1.5? for Planck WP. Allowing for larger ?m ? further reconciles the results. When we combine the SPTCL and Planck WP data sets with information from baryon acoustic oscillations and Type Ia supernovae, the preferred cluster masses are 1.9? higher than the Y X calibration and 0.8? higher than the ? v calibration. Given the scale of these shifts (~44% and ~23% in mass, respectively), we execute a goodness-of-fit test; it reveals no tension, indicating that the best-fit model provides an adequate description of the data. Using the multi-probe data set, we measure ?m = 0.299 ± 0.009 and ?8 = 0.829 ± 0.011. Within a ?CDM model we find ?m ? = 0.148 ± 0.081 eV. We present a consistency test of the cosmic growth rate using SPT clusters. Allowing both the growth index ? and the dark energy equation-of-state parameter w to vary, we find ? = 0.73 ± 0.28 and w = -1.007 ± 0.065, demonstrating that the expansion and the growth histories are consistent with a ?CDM universe (? = 0.55; w = -1).
