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We explore extensions to the $\Lambda$CDM cosmology using measurements of thecosmic microwave background (CMB) from the recent SPT-SZ survey, along withdata from WMAP7 and measurements of $H_0$ and BAO. We check for consistencywithin $\Lambda$CDM between these datasets, and find some tension. The CMBalone gives weak support to physics beyond $\Lambda$CDM, due to a slight trendrelative to $\Lambda$CDM of decreasing power towards smaller angular scales.While it may be due to statistical fluctuation, this trend could also beexplained by several extensions. We consider running index (nrun), as well astwo extensions that modify the damping tail power (the primordial heliumabundance $Y_p$ and the effective number of neutrino species $N_{\rm eff}$) andone that modifies the large-scale power due to the ISW effect (the sum ofneutrino masses $\sum m_\nu$). These extensions have similar observationalconsequences and are partially degenerate when considered simultaneously. Ofthe 6 one-parameter extensions considered, we find CMB to have the largestpreference for nrun with -0.046<nrun<-0.003 at 95% confidence, whichstrengthens to a 2.7$\sigma$ indication of nrun<0 from CMB+BAO+$H_0$.Detectable non-zero nrun is difficult to explain in the context ofsingle-field, slow-roll inflation models. We find $N_{\rm eff}=3.62\pm0.48$ forthe CMB, which tightens to $N_{\rm eff}=3.71\pm0.35$ from CMB+BAO+$H_0$. Largervalues of $N_{\rm eff}$ relieve the mild tension between CMB, BAO and $H_0$.When the SZ selected galaxy cluster abundances ($\rm{SPT_{CL}}$) data are alsoincluded, we obtain $N_{\rm eff}=3.29\pm0.31$. Allowing for $\sum m_\nu$ givesa 3$\sigma$ detection of $\sum m_\nu$>0 from CMB+BAO+$H_0$+$\rm{SPT_{CL}}$. Themedian value is $(0.32\pm0.11)$ eV, a factor of six above the lower bound setby neutrino oscillation observations. ... [abridged]

Constraints on Cosmology from the Cosmic Microwave Background Power Spectrum of the 2500 ${\rm deg}^2$ SPT-SZ Survey