Constraints on cosmology from the cosmic microwave background power spectrum of the 2500 deg² SPT-SZ survey

We explore extensions to the ΛCDM cosmology using measurements of the cosmic microwave background (CMB) from the recent SPT-SZ survey, along with data from WMAP7 and measurements of H ₀ and baryon acoustic oscillation (BAO). We check for consistency within ΛCDM between these data sets, and find some tension. The CMB alone gives weak support to physics beyond ΛCDM, due to a slight trend relative to ΛCDM of decreasing power toward smaller angular scales. While it may be due to statistical fluctuation, this trend could also be explained by several extensions. We consider running of the primordial spectral index (dn_s /dln k), as well as two extensions that modify the damping tail power (the primordial helium abundance Y_p and the effective number of neutrino species N _eff) and one that modifies the large-scale power due to the integrated Sachs-Wolfe effect (the sum of neutrino masses ∑m _ν). These extensions have similar observational consequences and are partially degenerate when considered simultaneously. Of the six one-parameter extensions considered, we find CMB to have the largest preference for dn_s /dln k with –0.046 < dn_s /dln k < –0.003 at 95% confidence, which strengthens to a 2.7σ indication of dn_s /dln k < 0 from CMB+BAO+H ₀. Detectable dn_s /dln k ≠ 0 is difficult to explain in the context of single-field, slow-roll inflation models. We find N _eff = 3.62 ± 0.48 for the CMB, which tightens to N _eff = 3.71 ± 0.35 from CMB+BAO+H ₀. Larger values of N _eff relieve the mild tension between CMB, BAO, and H ₀. When the Sunyaev-Zel'dovich selected galaxy cluster abundances (SPT_CL) data are also included, we obtain N _eff = 3.29 ± 0.31. Allowing for ∑m _ν gives a 3.0σ detection of ∑m _ν > 0 from CMB+BAO+H ₀ +SPT_CL. The median value is (0.32 ± 0.11) eV, a factor of six above the lower bound set by neutrino oscillation observations. All data sets except H ₀ show some preference for massive neutrinos; data combinations including H ₀ favor nonzero masses only if BAO data are also included. We also constrain the two-parameter extensions N _eff + ∑m _ν and N _eff + Y_p to explore constraints on additional light species and big bang nucleosynthesis, respectively.