Late-time Background Constraints on Linear and Non-linear Interacting Dark Energy after DESI DR2

TL;DR

The paper tackles whether phenomenological interacting dark energy (IDE) scenarios, with analytic $H(z)$ solutions, can improve fits to late-time cosmological data beyond ΛCDM. It constrains eight IDE kernels (five linear and three non-linear) using Pantheon+ and DESI DR2, with extended runs including Cosmic Clocks and BBN priors, and assesses fit quality via Δχ^2 and ΔAIC, while examining effective equations of state and reconstructed w. The results predominantly favor DM-proportional couplings and reveal sign-switching energy transfer in several cases, accompanied by phantom-crossing in the effective dark energy equation of state; many models also predict negative dark energy densities in the past, illustrating potential physical challenges and the need for perturbation analyses. The study highlights IDE as a promising but intricate extension to the standard model, stressing caution in interpretation and the necessity to incorporate perturbations and early-time data to determine whether IDE can robustly address cosmological tensions.

Abstract

In this study, we present observational constraints on a class of phenomenological interacting dark energy (IDE) models that admit analytical solutions for the Hubble parameter $H(z)$. We consider a set of five linear and three non-linear IDE scenarios, encompassing both interactions proportional to the dark matter and/or dark energy densities, as well as non-linear combinations of the two. For all eight IDE models, we find a better fit than $Λ$CDM from a $Δχ^2$ analysis for both combinations of datasets considered. When using the Akaike Information Criterion ($Δ$AIC), we find a similarly improved fit in all cases, except for one dataset combination in $Q=3Hδρ_{\rm de}$. Our analysis also shows a preference for sign-switching interactions, with energy transfer from dark energy to dark matter at low redshift, reversing direction at higher redshift. These results should be interpreted with caution, as the latter direction of energy transfer is accompanied by negative dark energy densities in the past, which may be unphysical. Models that do not allow sign-changing behaviour instead show a preference for energy flow from dark matter to dark energy, and hence negative dark energy densities. The only exceptions are $Q=3Hδρ_{\rm de}$ and $Q=3Hδ\left(\tfrac{ρ_{\rm de}^2}{ρ_{\rm dm}+ρ_{\rm de}}\right)$, which exhibit energy flow in the opposite direction. Furthermore, for all interactions considered, we find a phantom-divide crossing in the effective dark energy equation of state $w^{\rm eff}_{\rm de}$, with the dark energy density decreasing ($w^{\rm eff}_{\rm de}>-1$) at present and at low redshift, while increasing ($w^{\rm eff}_{\rm de}<-1$) in the past at high redshift. These results highlight the promising, but problematic, nature of dark sector interactions, as well as the need to extend the analysis using early-time physics and datasets.

Figures (7)

• Figure 1: Pantheon+, DESI DR2, Cosmic Clocks & BBN – One-dimensional posterior distributions and two-dimensional contours obtained for several parameters for the reference $\Lambda$CDM model and the models given by $Q = 3\,H\,\delta\,\rho_{\mathrm{dm}}$ and $Q = 3\,H\,\delta\,\rho_{\mathrm{de}}$, discussed in Section \ref{['subsec:model_linear']}.
• Figure 2: Pantheon+, DESI DR2, Cosmic Clocks & BBN – One-dimensional posterior distributions and two-dimensional contours obtained for several parameters for the reference $\Lambda$CDM model and the models given by $Q = 3\,H\,\delta\,(\rho_{\mathrm{dm}}+\rho_{\mathrm{de}})$ and $Q = 3\,H\,\delta\,(\rho_{\mathrm{dm}}-\rho_{\mathrm{de}})$, discussed in Section \ref{['subsec:model_linear']}.
• Figure 3: Pantheon+, DESI DR2, Cosmic Clocks & BBN – One-dimensional posterior distributions and two-dimensional contours obtained for several parameters for the reference $\Lambda$CDM model and the models given by $Q=3H\delta \left( \frac{\rho_{\text{dm}} \rho_{\text{de}} }{\rho_{\text{dm}}+\rho_{\text{de}}} \right)$, $Q=3H\delta \left( \frac{\rho^2_{\text{dm}} }{\rho_{\text{dm}}+\rho_{\text{de}}} \right)$, and $Q=3H\delta \left( \frac{\rho^2_{\text{de}} }{\rho_{\text{dm}}+\rho_{\text{de}}} \right)$, discussed in Section \ref{['subsec:model_non_linear']}.
• Figure 4: Direction of energy transfer vs redshift for linear interactions, using the mean values obtained in Tables \ref{['tab:constraints_pantheon_desi']} and \ref{['tab:constraints_all_models']}. The direction of energy transfer is also summarised in Table \ref{['tab:Consequenses']}. Here we see that the most general form, $Q=3 H (\delta_{\text{dm}} \rho_{\text{dm}} + \delta_{\text{de}} \rho_{\text{de}})$, exhibits sign-switching behaviour. It behaves similarly to $Q=3 H \delta \rho_{\text{dm}}$ in the distant past, with a small relative energy flow from dark matter to dark energy, but behaves closer to $Q=3 H \delta \rho_{\text{de}}$ in the more recent past and the predicted future, where a larger relative energy flow from dark energy to dark matter is observed. This sign-changing behaviour, with similar initial and final directions of energy transfer, is also exhibited by $Q=3 H \delta (\rho_{\text{dm}}-\rho_{\text{de}})$. For $Q=3 H \delta (\rho_{\text{dm}}+\rho_{\text{de}})$, the coupling to dark matter is more prominent than the coupling to dark energy, causing the energy flow to resemble that of $Q=3 H \delta \rho_{\text{dm}}$. For all models, the relative interaction strength diminishes during radiation domination at very high redshift.
• Figure 5: Direction of energy transfer vs redshift for non-linear interactions, using the mean values obtained in Tables \ref{['tab:constraints_pantheon_desi']} and \ref{['tab:constraints_all_models']}. The direction of energy transfer is also summarised in Table \ref{['tab:Consequenses']}. For $Q=3H\delta \left( \frac{\rho_{\text{dm}}\rho_{\text{de}} }{\rho_{\text{dm}}+\rho_{\text{de}}} \right)$ and $Q=3H\delta \left( \frac{\rho^2_{\text{de}} }{\rho_{\text{dm}}+\rho_{\text{de}}} \right)$, the relative interaction strength diminishes at high redshift, when dark energy provides only a small contribution to the total energy density. Similarly, for $Q=3H\delta \left( \frac{\rho_{\text{dm}}\rho_{\text{de}} }{\rho_{\text{dm}}+\rho_{\text{de}}} \right)$ and $Q=3H\delta \left( \frac{\rho^2_{\text{dm}} }{\rho_{\text{dm}}+\rho_{\text{de}}} \right)$, which both involve energy transfer from dark matter to dark energy, the interaction becomes weaker in the future as the dark matter density becomes negligible.