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 - \alpha } 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 \alpha = 0.017 ^ { +0.030 } _ { -0.028 } , consistent with the standard model prediction of \alpha = 0 .
In combination with other published results , we constrain \alpha = 0.011 \pm 0.016 , an improvement of \sim 20 \% over published constraints .
This measurement also provides a strong constraint on the effective equation of state in models of decaying dark energy w _ { \mathrm { eff } } = -0.987 ^ { +0.016 } _ { -0.017 } .