Measuring the redshift dependence of the CMB monopole temperature with PLANCK data

We study the power of PLANCK data to constrain deviations of the Cosmic Microwave Background black body temperature from adiabatic evolution using the thermal Sunyaev-Zeldovich anisotropy induced by clusters of galaxies. We consider two types of data sets: the cosmological signal is removed in the Time Ordered Information or is removed from the final maps; and two different statistical estimators, based on the ratio of temperature anisotropies at two different frequencies and on a fit to the spectral variation of the cluster signal with frequency. To test for systematics, we construct a template from clusters drawn from a hydro-simulation included in the pre-launch Planck Sky Model. We demonstrate that, using a proprietary catalog of X-ray selected clusters with measured redshifts, electron densities and X-ray temperatures, we can constrain deviations of adiabatic evolution, measured by the parameter $\alpha$ in the redshift scaling $T(z)=T_0(1+z)^{1-\alpha}$, with an accuracy of $\sigma_\alpha=0.011$ in the most optimal case and with $\sigma_\alpha=0.016$ for a less optimal case. These results represent a factor 2-3 improvement over similar measurements carried out using quasar spectral lines and a factor 6-20 with respect to earlier results using smaller cluster samples.