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We derive cosmological constraints using a galaxy cluster sample selectedfrom the 2500~deg$^2$ SPT-SZ survey. The sample spans the redshift range $0.25<z<1.75$ and contains 343 clusters with SZ detection significance $\xi>5$. Thesample is supplemented with optical weak gravitational lensing measurements of32 clusters with $0.29<z<1.13$ (from Magellan and HST) and X-ray measurementsof 89 clusters with $0.25<z<1.75$ (from Chandra). We rely on minimal modelingassumptions: i) weak lensing provides an accurate means of measuring halomasses, ii) the mean SZ and X-ray observables are related to the true halo massthrough power-law relations in mass and dimensionless Hubble parameter $E(z)$with a-priori unknown parameters, iii) there is (correlated, lognormal)intrinsic scatter and measurement noise relating these observables to theirmean relations. We simultaneously fit for these astrophysical modelingparameters and for cosmology. Assuming a flat $\nu\Lambda$CDM model, in whichthe sum of neutrino masses is a free parameter, we measure$\Omega_\mathrm{m}=0.276\pm0.047$, $\sigma_8=0.781\pm0.037$, and$\sigma_8(\Omega_\mathrm{m}/0.3)^{0.2}=0.766\pm0.025$. The redshift evolutionof the X-ray $Y_\mathrm{X}$-mass and $M_\mathrm{gas}$-mass relations are bothconsistent with self-similar evolution to within $1\sigma$. The mass-slope ofthe $Y_\mathrm{X}$-mass relation shows a $2.3\sigma$ deviation fromself-similarity. Similarly, the mass-slope of the $M_\mathrm{gas}$-massrelation is steeper than self-similarity at the $2.5\sigma$ level. In a $\nuw$CDM cosmology, we measure the dark energy equation of state parameter$w=-1.55\pm0.41$ from the cluster data. We perform a measurement of the growthof structure since redshift $z\sim1.7$ and find no evidence for tension withthe prediction from General Relativity. We provide updated redshift and massestimates for the SPT sample. (abridged)

astrophysical journal/the astrophysical journal

Cluster Cosmology Constraints from the 2500 deg$^2$ SPT-SZ Survey:  Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble  Space Telescope