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 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 ∼2 σ are observed. Additionally, we identify a mild but noteworthy tension, also at the ∼2 σ level, between our GP inferred value of the present-day CMB temperature, T 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 α , which could provide a physical explanation for the observed deviations at low redshift.