| Summary: | The adiabatic evolution of the temperature of the cosmic microwave background (CMB) is a key prediction of standard cosmology. We study deviations from the expected adiabatic evolution of the CMB temperature of the form T(z) = T_0(1 + z)^(1 − α) using measurements of the spectrum of the Sunyaev–Zel'dovich effect with the South Pole Telescope (SPT). We present a method for using the ratio of the Sunyaev–Zel'dovich signal measured at 95 and 150 GHz in the SPT data to constrain the temperature of the CMB. We demonstrate that this approach provides unbiased results using mock observations of clusters from a new set of hydrodynamical simulations. We apply this method to a sample of 158 SPT-selected clusters, spanning the redshift range 0.05 < z < 1.35, and measure α=0.017^(+0.030)_(−0.028), consistent with the standard model prediction of α = 0. In combination with other published results, we find α = 0.005 ± 0.012, an improvement of ∼10 per cent over published constraints. This measurement also provides a strong constraint on the effective equation of state in models of decaying dark energy w_(eff) = −0.994 ± 0.010. © 2014 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2014 February 19. Received 2014 February 17; in original form 2013 December 7. The Munich SPT group is supported by the DFG through TR33 'The Dark Universe' and the Cluster of Excellence 'Origin and Structure of the Universe'. The South Pole Telescope programme is supported by the National Science Foundation through grant ANT-0638937. Partial support is also provided by the NSF Physics Frontier Center grant PHY-0114422 to the Kavli Institute of Cosmological Physics at the University of Chicago, by the Kavli Foundation and the Gordon and Betty Moore Foundation and by NASA grant number PF2-130094. Galaxy cluster research at Harvard is supported by NSF grants AST-1009012 and DGE-1144152. Galaxy cluster research at SAO is supported in part by NSF grants AST-1009649 and ...
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