Revisiting the temperature evolution law of the CMB with gaussian processes

In this work, we perform a statistical inference of the classical background law governing the evolution of the temperature of the cosmic microwave background radiation (CMB), given by $T_{\rm CMB}(z) = T_0(1 + z)$. To this end, we employ Gaussian Process (GP) regression techniques to reconstruct the temperature evolution based on two observational datasets: (i) CMB-Sunyaev-Zel'dovich (SZ) cluster measurements and (ii) CMB-interstellar medium (ISM) interaction data. Our analysis reveals interesting results that may suggest potential deviations from the standard temperature-redshift relation, particularly at low redshifts ($z < 0.5$), where discrepancies up to $\sim$2$\sigma$ are observed. Additionally, we identify a mild but noteworthy tension, also at the $\sim$2$\sigma$ level, between our GP inferred value of the present-day CMB temperature, $T_{\rm CMB}(z=0)$, and the precise direct measurement from the COBE/FIRAS experiment. We also explore possible phenomenological implications of our findings, including interpretations associated with possible variations in fundamental constants, such as the fine-structure constant $\alpha$, which could provide a physical explanation for the observed deviations at low redshift.