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 (σ 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 σ v and Y X are consistent at the 0.6σ level, with the σ v calibration preferring ~16% higher masses. We use the full SPTCL data set (SZ clusters+σ v +Y X) to measure σ8(Ωm/0.27)0.3 = 0.809 ± 0.036 within a flat ΛCDM 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 ν = 0.06 eV, we find the data sets to be consistent at the 1.0σ level for WMAP9 and 1.5σ for Planck+WP. Allowing for larger ∑m ν 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 1.9σ higher than the Y X calibration and 0.8σ higher than the σ 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 Ωm = 0.299 ± 0.009 and σ8 = 0.829 ± 0.011. Within a νCDM model we find ∑m ν = 0.148 ± 0.081 eV. We present a consistency test of the cosmic growth rate using SPT clusters. Allowing both the growth index γ and the dark energy equation-of-state parameter w to vary, we find γ = 0.73 ± 0.28 and w = -1.007 ± 0.065, demonstrating that the expansion and the growth histories are consistent with a ΛCDM universe (γ = 0.55; w = -1).
