New constraints on interacting dark energy from DESI DR2 BAO observations

This paper asks how new Baryon Acoustic Oscillation (BAO) measurements from DESI Data Release 2 (DR2) constrain models in which dark energy (DE) and dark matter (DM) exchange energy non-gravitationally, i.e., interacting dark energy (IDE) scenarios. The question matters because the standard $\Lambda$CDM model is increasingly challenged by “tensions” between parameter values inferred from different cosmological probes—most notably the Hubble constant tension ( $H_0$) and the clustering amplitude tension often summarized by $S_8$. IDE models are a popular extension because, with an appropriate sign and magnitude of the coupling, they can shift late-time expansion and growth in ways that may reduce these discrepancies. However, a recurring difficulty is that improving one tension often worsens another. The authors therefore test not only a traditional constant-sign IDE model, but also a recently proposed sign-switching IDE (S-IDE) model in which the direction of energy transfer reverses at a characteristic “dark-sector equality” redshift.

The study’s significance is twofold. First, it leverages DESI DR2 BAO data, which cover a wide redshift range ( $0.295\le z\le 2.330$) and are based on extremely large samples (over 13.1 million galaxies and 1.6 million quasars). This improves the geometric leverage on the expansion history and, through the coupled dynamics, on the inferred interaction strength. Second, it performs model comparison and joint inference across multiple late-time probes—BAO plus cosmic microwave background (CMB) plus carefully selected Type Ia supernova (SN Ia) datasets—while explicitly addressing dataset compatibility (tension avoidance) via a selection strategy for the S-IDE case.

Methodologically, the authors implement both IDE frameworks in the CLASS Boltzmann solver and use MontePython to run Markov Chain Monte Carlo (MCMC) parameter inference. Convergence is checked with the Gelman -Rubin criterion, requiring $R-1\le 10^{-2}$ in all runs. The parameter space includes the six standard $\Lambda$CDM parameters ( ${\omega }_b$, ${\omega }_c$, $100{\theta }_s$, $\ln (10^{10}{A}_s)$, $n_s$, ${\tau }_{\mathrm{reio}}$) plus an interaction coupling parameter. For the traditional IDE model, the coupling is a constant $\xi$ (sampled with a prior range $[-1,0]$). For S-IDE, the coupling is sign-switching and parameterized by an initial amplitude ${\xi }_i$ with a broader prior $[-1.5,1.5]$. The sign-switching behavior is encoded through $\xi (z)={\xi }_i\mathrm{sgn}(z_{\mathrm{eq},\mathrm{dark}}-z)$, where $z_{\mathrm{eq},\mathrm{dark}}$ depends on the density ratio at which matter and DE are equal in the interacting model.

The likelihood inputs are: (1) Planck 2018 CMB temperature and polarization likelihoods (high- $\ell$ Plik TT/TE/EE plus low- $\ell$ SimAll TT-only and EE-only) and CMB lensing reconstruction; (2) DESI DR2 BAO measurements, including isotropic and anisotropic BAO constraints in nine redshift bins and incorporating cross-correlation coefficients between BAO distance measures; and (3) SN Ia datasets: PantheonPlus (PP), a calibrated variant PantheonPlus&SH0ES (PPS) using Cepheid-based anchors, Union 3.0 (Union3), and DESY5. The authors also use the Akaike Information Criterion (AIC) for model comparison, defined as $\mathrm{AIC}=-2\ln L_{\max }+2N$, where the penalty term discourages overfitting.

Key findings for the traditional IDE model are reported primarily in terms of the coupling $\xi$, the inferred $H_0$, and $S_8$. With CMB+DESI-DR2 alone, the coupling is negative and only moderately preferred: $\xi =-0.132_{-0.064}^{+0.087}$ (about $\sim 1\sigma$ evidence), with a 95% lower bound $\xi >-0.254$. When adding the PPS SN sample (CMB+DESI-DR2+PPS), the coupling becomes more tightly constrained and remains negative: $\xi =-0.116_{-0.050}^{+0.060}$ at 68% CL, with $H_0=69.61\pm 0.44$ km/s/Mpc. This combination yields an approximately $\sim 2\sigma$ indication of a dark-sector coupling and reduces the Hubble tension to moderate levels (quoted as $\sim 3\sigma$ in the PPS case and $\sim 2.7\sigma$ for the CMB+DESI-DR2-based combination). In terms of clustering, the traditional IDE model is described as compatible with the latest cosmic shear constraints on $S_8$ (e.g., KiDS Legacy), with $S_8$ values around $0.85$ for CMB+DESI-DR2+PPS ( $S_8=0.850_{-0.028}^{+0.020}$).

A central practical point emphasized by the authors is that SN data strongly tighten the coupling constraints. Across SN combinations appended to CMB+DESI-DR2, they obtain direct lower bounds on $\xi$ (i.e., excluding too-negative coupling) of $\xi >-0.0538$ with PP, $\xi >-0.0220$ with DESY5, and $\xi >-0.0630$ with Union3. The strongest and most up-to-date constraint is claimed for the CMB+DESI-DR2+DESY5 analysis.

For the S-IDE model, the authors adopt a dataset selection strategy to avoid significant tension with the primary CMB+DESI-DR2 combination: they note that CMB+PPS has only a $0.10\sigma$ tension, while CMB+PP, CMB+Union3, and CMB+DESY5 can reach discrepancies up to $4.64\sigma$ (and thus could bias the inference). Under CMB+DESI-DR2, the coupling is $\xi =-0.109\pm 0.091$ (68% CL) and $H_0=69.05\pm 0.46$ km/s/Mpc, with $S_8=0.796\pm 0.012$. Adding PPS (CMB+DESI-DR2+PPS) yields $\xi =-0.167\pm 0.080$, which the authors interpret as mild evidence for a non-zero coupling at the $\sim 2\sigma$ level. In this PPS-anchored S-IDE case, $H_0=69.46\pm 0.38$ km/s/Mpc and $S_8=0.7886\pm 0.0099$, i.e., lower $S_8$ than in the traditional IDE model.

The paper also reports model-comparison statistics. For traditional IDE, the AIC and $\Delta {\chi }_{\min }^2$ values vary by dataset combination; for example, CMB+DESI-DR2+PPS gives $\Delta {\chi }_{\min }^2=-2.20$ and $\Delta \mathrm{AIC}=-0.20$, indicating a slight preference for IDE over $\Lambda$CDM when accounting for parameter count. For S-IDE, the CMB+DESI-DR2 combination has $\Delta {\chi }_{\min }^2=0.14$ and $\Delta \mathrm{AIC}=2.14$, while CMB+DESI-DR2+PPS yields $\Delta {\chi }_{\min }^2=-3.26$ and $\Delta \mathrm{AIC}=-1.26$, suggesting that PPS calibration drives the improvement.

The authors connect these parameter shifts to the BAO residuals and to the reconstructed expansion history. They provide a redshift-bin-by-bin residual comparison (in units of observational uncertainty) showing that S-IDE often yields residuals comparable to or smaller than $\Lambda$CDM and traditional IDE, with notable examples such as at $z=0.934$ in the $z{D}_H(z)/(r_d\sqrt{z})$ observable where S-IDE gives $+0.28\sigma$ versus $+0.59\sigma$ for $\Lambda$CDM and $+0.40\sigma$ for IDE. They also emphasize that S-IDE’s effective equation of state transitions dynamically, with $w_{\mathrm{eff}}(z)=-1+\xi (z)$, moving from a phantom-like regime to a quintessence-like regime across $z_{\mathrm{eq},\mathrm{dark}}$. The inferred transition redshift is $z_{\mathrm{eq},\mathrm{dark}}=0.297_{-0.028}^{+0.021}$ for CMB+DESI-DR2 and $0.287_{-0.023}^{+0.017}$ when PPS is included.

Limitations are acknowledged in two ways. First, the authors stress that the apparent alleviation of tensions—especially in S-IDE—depends sensitively on the choice of SN dataset, particularly the PPS calibration anchored to Cepheids. They explicitly caution that without this calibration, S-IDE is generally disfavored relative to $\Lambda$CDM. Second, they note that growth-tension comparisons involving $S_8$ from redshift-space distortions (RSD) and full-shape galaxy clustering are model-dependent; they therefore treat the quantitative “tension reduction” with caution and call for re-analysis under the interacting model.

Practically, the results suggest that DESI DR2 BAO data, when combined with CMB and carefully selected SN Ia samples, can tighten constraints on dark-sector coupling and can shift inferred $H_0$ and $S_8$ in directions that reduce (but do not fully eliminate) the Hubble tension. The traditional IDE model appears to remain compatible with cosmic shear $S_8$ constraints, while S-IDE naturally allows lower $S_8$ values that may better align with some alternative views of the $S_8$ tension. Who should care includes cosmologists interpreting late-time probes and model builders assessing whether interacting dark-sector phenomenology can remain viable under increasingly precise DESI-era BAO constraints.

Overall, the paper’s core contribution is an updated, DESI-DR2-driven parameter inference for interacting dark energy models, showing that both traditional IDE and sign-switching S-IDE can moderate the $H_0$ tension to roughly the $\sim 2.7\sigma$ level, with the strongest coupling evidence and best model preference occurring when SN calibration (PPS) is included—while S-IDE also offers a dynamical transition in the effective equation of state consistent with DESI-DR2 qualitative preferences for $w_0>-1$.