Resilience and implications of adiabatic CMB cooling

We investigate potential deviations from the standard adiabatic evolution of the cosmic microwave background (CMB) temperature, $T_{\rm CMB}(z)$, using the latest Sunyaev-Zeldovich (SZ) effect measurements and molecular line excitation data, covering a combined redshift range of $0 < z \lesssim 6$. We follow different approaches. First, we reconstruct the redshift evolution of $T_{\rm CMB}(z)$ in a model-independent way using Gaussian Process regression. The tightest constraints come from SZ measurements at $z < 1$, while molecular line data at $z > 3$ yield broader uncertainties. By combining both datasets, we find good consistency with the standard evolution across the full analysed redshift range, inferring a present-day CMB monopole temperature of $T_0 = 2.744 \pm 0.019$ K. Next, we test for deviations from the standard scaling by adopting the parameterisation $T_{\rm CMB}(z) = T_0(1+z)^{1-\beta}$, where $\beta$ quantifies departures from adiabaticity, with $\beta = 0$ corresponding to the standard scenario. In this framework, we use Gaussian Process reconstruction to test the consistency of $\beta = 0$ across the full redshift range and perform $\chi^2$ minimisation techniques to determine the best-fit values of $T_0$ and $\beta$. In both cases, we find good consistency with the standard temperature-redshift relation. The $\chi^2$-minimisation analysis yields best-fit values of $\beta = -0.0106 \pm 0.0124$ and $T_0 = 2.7276 \pm 0.0095$ K, in excellent agreement with both $\beta = 0$ and independent direct measurements of $T_0$ from FIRAS and ARCADE. We discuss the implications of our findings, which offer strong empirical support for the standard cosmological prediction and place tight constraints on a wide range of alternative scenarios of interest in the context of cosmological tensions and fundamental physics.