Resilience and implications of adiabatic CMB cooling

TL;DR

This work tests the standard adiabatic cooling of the CMB by combining SZ-based and molecular-line measurements of $T_{\rm CMB}(z)$ over $0<z\lesssim6$. It employs Gaussian Process reconstructions to model $T_{\rm CMB}(z)$ in a model-independent way and also explores deviations via the parametric form $T_{\rm CMB}(z)=T_0(1+z)^{1-\beta}$, determining $T_0$ and $\beta$ through both GP and $\chi^2$ analyses. The results show strong agreement with the standard scaling, yielding $T_0$ values of $2.744\pm0.019$ K (GP) and $2.7276\pm0.0095$ K (χ^2), and a null deviation parameter $\beta\approx0$ within uncertainties, thereby constraining a broad class of non-adiabatic or photon-number-violating scenarios. These findings reinforce the standard cosmological model, limit potential connections to the DDR and Hubble tension, and guide future explorations with upcoming facilities that will sharpen tests of the CMB thermal history.

Abstract

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 $T_{\rm CMB}(z) = T_0(1+z)^{1-β}$, where $β$ quantifies departures from adiabaticity, with $β= 0$ corresponding to the standard scenario. In this framework, we use Gaussian Process reconstruction to test the consistency of $β= 0$ across the full redshift range and perform $χ^2$ minimisation techniques to determine the best-fit values of $T_0$ and $β$. In both cases, we find good consistency with the standard temperature-redshift relation. The $χ^2$-minimisation analysis yields best-fit values of $β= -0.0106 \pm 0.0124$ and $T_0 = 2.7276 \pm 0.0095$ K, in excellent agreement with both $β= 0$ 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.

Figures (5)

• Figure 1: Illustration of the number of Sunyaev-Zeldovich (SZ) effect and spectroscopic (Spec) measurement data points at different redshift bins. For creating a clear visual separation, the placement of bars follows a specific arrangement: the SZ data are placed at the bin centre minus 0.5 bar width and the Spec data at the bin centre plus 0.5 bar width. This strategic offset between the two datasets within each bin allows for easy comparison of data availability across the entire redshift range.
• Figure 2: Reconstruction of $T_{\rm CMB}(z)$ through GP as a function of redshift. The increasingly lighter shaded pink regions represent the $1\sigma$, $2\sigma$ and $3\sigma$ confidence intervals. The reconstruction is performed considering only the SZ data (left panel, blue circles) and the spectroscopic measurements (middle panel, green squares), as well as their combination (right panel).
• Figure 3: Reconstructed evolution of the deviation parameter $\beta$ as a function of redshift using Gaussian Processes regression applied to the observational CMB temperature datasets. The increasingly lighter pink regions represent the $1\sigma$, $2\sigma$ and $3\sigma$ confidence intervals of the reconstruction, illustrating potential redshift-dependent behaviour of the deviation from the standard cosmological scaling ($\beta=0$). The reconstruction is performed considering only the SZ data (left panel, blue circles) and the spectroscopic measurements (middle panel, green squares), as well as their combination (right panel).
• Figure 4: Comparison between the best-fit prediction for $T_{\rm CMB}(z)$ under the standard temperature-redshift evolution in \ref{['eq:tz_scal']} (black) and the $\beta$-scaling power-law model in \ref{['eq:tzbeta_scal']} (pink). The analysis is performed considering only the SZ data (left panel, blue circles), the spectroscopic measurements (middle panel, green squares), as well as their combination (right panel). The lower panels show the normalised residuals in each case.
• Figure 5: Whisker plot displaying several notable $T_0$ determinations from the literature, each obtained using different methodologies and datasets as described in the text. The results derived in this work are presented at the top of the figure under the label Ruchika et al. (2025), with the value inferred from GP reconstruction shown in purple and the one from the $\chi^2$ analysis shown in blue. The FIRAS and ARCADE results are represented in red and orange, respectively, at the bottom of the figure. For context, additional estimates from previous studies are shown in black. All uncertainties are quoted at the 68% confidence level. The upper panel of the plot displays the full 1D posterior distributions of our results and the direct estimates from FIRAS and ARCADE for comparison.