Measurement of the $T_{\mathrm{C}\mathrm{M}\mathrm{B}}$ evolution from the Sunyaev-Zel'dovich effect

In the standard hot cosmological model, the black-body temperature of the Cosmic Microwave Background (CMB), $T_{\mathrm{C}\mathrm{M}\mathrm{B}}$, increases linearly with redshift. Across the line of sight CMB photons interact with the hot ($\sim {10}^{7-8}$ K) and diffuse gas of electrons from galaxy clusters. This interaction leads to the well known thermal Sunyaev-Zel’dovich effect (tSZ), which produces a distortion of the black-body emission law, depending on $T_{\mathrm{C}\mathrm{M}\mathrm{B}}$. Using tSZ data from the $Planck$ satellite it is possible to constrain $T_{\mathrm{C}\mathrm{M}\mathrm{B}}$ below z=1. Focusing on the redshift dependance of $T_{\mathrm{C}\mathrm{M}\mathrm{B}}$ we obtain $T_{\mathrm{C}\mathrm{M}\mathrm{B}}(z)=(2.726\pm 0.001)\times (1+z{)}^{1-\beta }$ K with $\beta =0.009\pm 0.017$, improving previous constraints. Combined with measurements of molecular species absorptions, we derive $\beta =0.006\pm 0.013$. These constraints are consistent with the standard (i.e. adiabatic, $\beta =0$) Big-Bang model.