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(abridged) We present cosmological constraints obtained from galaxy clustersidentified by their Sunyaev-Zel'dovich effect signature in the 2500 squaredegree South Pole Telescope Sunyaev Zel'dovich survey. We consider the 377cluster candidates identified at z>0.25 with a detection significance greaterthan five, corresponding to the 95% purity threshold for the survey. We computeconstraints on cosmological models using the measured cluster abundance as afunction of mass and redshift. We include additional constraints frommulti-wavelength observations, including Chandra X-ray data for 82 clusters anda weak lensing-based prior on the normalization of the mass-observable scalingrelations. Assuming a LCDM cosmology, where the species-summed neutrino masshas the minimum allowed value (mnu = 0.06 eV) from neutrino oscillationexperiments, we combine the cluster data with a prior on H0 and find sigma_8 =0.797+-0.031 and Omega_m = 0.289+-0.042, with the parameter combinationsigma_8(Omega_m/0.27)^0.3 = 0.784+-0.039. These results are in good agreementwith constraints from the CMB from SPT, WMAP, and Planck, as well as withconstraints from other cluster datasets. Adding mnu as a free parameter, wefind mnu = 0.14+-0.08 eV when combining the SPT cluster data with Planck CMBdata and BAO data, consistent with the minimum allowed value. Finally, weconsider a cosmology where mnu and N_eff are fixed to the LCDM values, but thedark energy equation of state parameter w is free. Using the SPT cluster datain combination with an H0 prior, we measure w = -1.28+-0.31, a constraintconsistent with the LCDM cosmological model and derived from the combination ofgrowth of structure and geometry. When combined with primarily geometricalconstraints from Planck CMB, H0, BAO and SNe, adding the SPT cluster dataimproves the w constraint from the geometrical data alone by 14%, to w =-1.023+-0.042.

Cosmological Constraints from Galaxy Clusters in the 2500 square-degree SPT-SZ Survey