Dynamical Dark Energy models in light of the latest observations

TL;DR

The paper systematically tests a broad set of dynamical dark energy models against state-of-the-art cosmological data using CLASS/Cobaya, focusing on Planck PR4, DESI DR2 BAO, and two SNIa samples (PantheonPlus and DES-Y5) without SH0ES priors. By comparing running vacuum variants (RVM, RRVM, RVM$_{\rm thr}$, flipped RVM) with interactive DE–DM scenarios ($Q_{\rm dm}$, $Q_{\Lambda}$), the two-component wXCDM, and the CPL parameterization, the authors quantify evidence for dynamical DE via AIC, DIC, and likelihood-ratio tests. They find mild hints of dynamical DE (≈2σ) in several interacting models with PantheonPlus+DESI, while the DES-Y5 dataset amplifies the signal, pushing CPL and flipped RVM to exclusions of $\Lambda$CDM at ≈4σ (AIC) and ≈3σ (DIC/LR context), with notable suppression in structure growth in some models. The results imply nontrivial DE evolution and possible dark sector interactions, and they highlight the role of growth data in future discrimination among competing dynamical DE scenarios.

Abstract

In this paper, we study several models and parameterizations of dynamical dark energy (DE) that have been studied already in the past, in conjunction with the recently proposed model $w$XCDM, the running vacuum model (RVM) with and without a threshold at $z=1$ and two variants of it, the RRVM and the ``flipped RVM'', and compare them all with the concordance $Λ$CDM model and the popular $w_0w_a$CDM parameterization. We use two standard sets of cosmological data, one including distant supernovae from Pantheon$+$ and the other from DES-Y5. The rest of the data (BAO from DESI DR2 and CMB from Planck PR4) are shared by the two sets. They are analyzed with the help of \texttt{CLASS}. No structure formation data are utilized for this analysis and no use is made of the SH0ES calibration of $H_0$. Even so, we find that the flipped RVM and to a lesser extent the $w$XCDM and the RVM with threshold, point to significant evidence of dynamical DE, at a level comparable to $w_0w_a$CDM, more conspicuously for the dataset that involves DES-Y5 observations. We also find that while more traditional models studied in the past, in which there is an exchange between vacuum energy and cold dark matter (through e.g. an interactive source proportional either to the density of dark matter or to that of vacuum) still hint at dynamical DE, the strength of the statistical signal (which we assess through information criteria and other estimators) is nevertheless less pronounced. Finally, we discuss the ability of the various models to explain the data by performing an analysis of their effective equation-of-state parameters and corresponding evolution of their dark energy densities.

Figures (3)

• Figure 1: The effective DE density, $\tilde{\rho}_{\rm de}(z)$, and EoS parameter, $w_{\rm eff,de}(z)$, are shown as defined in Eqs. \ref{['eq:effectiveDens']} and \ref{['eq:effectiveEoS']}, respectively, using the best-fit values of the various models under study obtained in the analyses with CMB+PantheonPlus+DESI (upper row) and CMB+DES-Y5+DESI (lower row). We normalize the effective DE density to the energy density associated with the cosmological constant in the $\Lambda$CDM model, $\rho_{\rm vac}=\Lambda/(8\pi G_N)$, as inferred from Planck PR4 data Rosenberg:2022sdy. We also display, in light blue, the $68\%$ and $95\%$ CL bands obtained in Gonzalez-Fuentes:2025lei using a model-independent approach, the so-called Weighted Function Regression method Gomez-Valent:2018hwcGomez-Valent:2018gvm. Note that most of the considered DE models, except $Q_{\rm dm}$ and RRVM (without threshold), exhibit a phantom divide crossing. See the main text for the important implications of this fact.
• Figure 2: Exclusion level $E_{\Lambda{\rm CDM}}=\xi\times\sigma$ -- see Eq. \ref{['eq:pvalue']} -- of the standard model $\Lambda$CDM with respect to the dynamical DE models that are nested to the former, obtained from the fitting analyses with CMB+PantheonPlus+DESI (left plot) and CMB+DES-Y5+DESI (right plot).
• Figure 3: Posterior distributions of the parameter $\nu_i$ that controls the transfer of energy between the vacuum and dark matter in the various interacting models (cf. Sec. \ref{['sec:models']}), obtained with the datasets CMB+PantheonPlus+DESI (dashed curves) and CMB+DES-Y5+DESI (solid curves). In the figure, abscissas denotes the parameter $\nu$ of the RVM$_{\rm thr}$ and RRVM, but also $\nu_\Lambda$ and $\nu_{\rm dm}$ of $Q_\Lambda$ and $Q_{\rm dm}$, respectively.