Dark Degeneracy in DESI DR2: Interacting or Evolving Dark Energy?

TL;DR

The paper investigates a background-degenerate correspondence between dynamical dark energy (CPL) and an interacting dark-energy (IDE) model using DESI DR2 BAO, DESY5 SN, Planck, and ACT data. By fixing the background expansion to be identical, it tests whether perturbations can distinguish the two mechanisms, implementing a mapping between $\bar{w}_x(a)$ and $\tilde{f}(\tilde{r})$ and analyzing linear perturbations with $c_s^2=1$ and no perturbation in Q. The results show both models fit the data better than $\Lambda$CDM, with the IDE model predicting a higher present-day matter density $\Omega_m$ and a lower $\sigma_8$, driven by a late-time sign-change in the interaction around $z\approx0.8$, potentially alleviating the $S_8$ tension but conflicting with growth-rate measurements $f\sigma_8$. The work highlights that background degeneracy does not guarantee observational indistinguishability once structure growth is included, emphasizing the need for combining expansion-history probes with growth and lensing observations to assess viability of such dark-sector scenarios.

Abstract

The standard $Λ$CDM model, despite its success, is challenged by persistent observational tensions in the Hubble constant ($H_0$) and the matter clustering amplitude ($S_8$), motivating the exploration of alternative cosmological scenarios. We investigate a dark energy model with a phenomenological interaction in the dark sector, constructed to be exactly degenerate at the background level with the Chevallier-Polarski-Linder (CPL) parameterization. This setup allows us to test whether models with identical expansion histories but distinct physical mechanisms can be distinguished by cosmological data. We perform a Bayesian analysis using a combination of recent datasets: DESI DR2 BAO measurements, DESY5 supernovae, and CMB data from Planck and ACT. We find that both the interacting model and the CPL model provide significantly better fits to the data than $Λ$CDM. Although indistinguishable in background observables, the interacting model predicts a distinct matter-sector evolution driven by a late-time sign change in the dark sector interaction at $z \approx 0.8$, corresponding to the $w=-1$ crossing in the CPL description. In this sense, the interacting picture may be considered more physical, since it avoids the problematic crossing by construction. The resulting decay of dark energy into dark matter lowers $S_8$, potentially alleviating the weak-lensing $S_8$ tension. At the same time, it predicts a sharp suppression of the growth rate $fσ_8(z)$ at $z \lesssim 0.8$, which is in tension with current measurements of structure formation. This indicates that the model may not simultaneously reconcile the expansion history and the observed growth of cosmic structure, highlighting the need for a more comprehensive analysis to fully assess its viability.

Figures (8)

• Figure 1: The 68% and 95% C.L. posterior contours for the $(w_0, w_a)$ parameters. The CPL model is shown in red, and the Interaction model in blue. The black dashed lines indicate the $\Lambda$CDM model, which is excluded at high significance.
• Figure 2: The 68% and 95% C.L. posterior contours for $H_0$, $\Omega_m$, and $\sigma_8$. The results for $\Lambda$CDM, CPL, and the Interaction model are shown.
• Figure 3: The 68% and 95% C.L. posterior contours for the early-Universe parameters: the angular acoustic scale ($\theta_s$), scalar amplitude ($\log(10^{10}A_s)$), spectral index ($n_s$), and optical depth to reionization ($\tau_{\mathrm{reio}}$).
• Figure 4: Evolutions of the CPL and IDE best-fit models.
• Figure 5: Comparison of the background expansion history for the CPL and Interaction models, relative to the best-fit $\Lambda$CDM model. The points in the top and center panels are from DESI:2025zgx.