Probing Dynamical Dark Energy with Late-Time Data: Evidence, Tensions, and the Limits of the $w_0w_a$CDM Framework

TL;DR

This work tests the dynamical dark energy CPL model against ΛCDM by combining Planck+ACT CMB data with diverse late-time distance probes (BAOtr, DESI DR2 BAO, SDSS BAO, and PantheonPlus SN Ia with SH0ES calibration). Using a Bayesian Cobaya/PolyChord framework, it explores the CPL parameters $w_0$ and $w_a$, along with derived quantities such as $H_0$, $r_d$, and $r_dH_0$, and evaluates model evidence across dataset combinations. The key finding is that CPL inferences are highly dataset-dependent: CMB-only allows a phantom-like tail in the deceleration parameter $q_0$, DESI BAO pulls toward a near-coasting expansion, and combinations with PP&SH0ES and BAOtr yield moderate acceleration and substantial relief of the Hubble tension. Importantly, the sound horizon $r_d$ remains nearly unchanged across datasets, implying that shifts in $H_0$ arise from late-time expansion freedom rather than early-Universe physics, while BAO datasets exhibit intrinsic tensions that challenge a universal CPL background. The results highlight limitations of the two-parameter CPL description and motivate either more flexible late-time models or a careful reassessment of low-redshift BAO systematics to ensure robust inferences about dark energy dynamics.

Abstract

We test the dynamical dark-energy $w_0w_a$CDM (CPL) framework against $Λ$CDM using CMB anisotropies and lensing together with late-time distance probes: DESI DR2 BAO, the completed SDSS-IV BAO consensus compilation, a transverse/angular BAO compilation (BAOtr), and the Cepheid-calibrated PantheonPlus SN~Ia likelihood (PP\&SH0ES). We find that CPL inferences are strongly dataset-dependent. With CMB data alone, the broad geometric degeneracy in $(H_0,Ω_{\rm m},w_0,w_a)$ admits an extrapolation tail that can extend to $q_0<-1$ (super-acceleration), whereas adding DESI DR2 BAO pulls the reconstruction toward a weakly accelerating or nearly coasting present-day Universe ($q_0\simeq 0$). In contrast, combining CMB with PP\&SH0ES and BAOtr yields a conventional moderately accelerating expansion ($-1<q_0\lesssim 0$) and substantially reduces the Hubble tension. Across all combinations, $w(z\to\infty)=w_0+w_a<-1$, while at post-recombination redshifts the expansion remains matter dominated ($q\to1/2$). The origin of this behavior can be traced to low-redshift distance information: BAOtr and DESI prefer different BAO distance ratios at $z\lesssim 0.5$, which propagates into divergent expansion histories in CPL. In all cases, $r_{\rm d}$ stays nearly unchanged, indicating that shifts in $H_0$ arise from late-time expansion freedom rather than early-Universe physics. Bayesian evidence mirrors this contingency: it is strong for CPL mainly when PP\&SH0ES and/or BAOtr are included, while it is inconclusive for CMB-only and CMB+DESI and moderately favors $Λ$CDM for CMB+SDSS. Overall, our results show that the apparent support for CPL and its ability to ease the Hubble tension are not universal but depend sensitively on the adopted low-redshift distance data, motivating either more flexible late-time models or closer scrutiny of residual systematics in current BAO determinations.

Figures (9)

• Figure 1: Two-dimensional marginalized posteriors in the $w_0w_a$CDM (CPL) model showing the correlations among $(w_0,w_a,H_0)$ for the dataset combinations listed in the legend. Panels show $(w_0,w_a)$ (left), $(w_0,H_0)$ (middle), and $(w_a,H_0)$ (right). The red horizontal bands in the $H_0$ panels indicate the H0DN determination H0DN:2025lyy at $\pm1\sigma$ and $\pm2\sigma$ for reference. Contours enclose 68% and 95% credible regions.
• Figure 2: Hubble-constant tension with respect to the H0DN determination, shown for each dataset combination in $\Lambda$CDM (left) and $w_0w_a$CDM (right). For each case, we form the difference distribution $\Delta H_0 = H_0^{\rm (case)} - H_0^{\rm (H0DN)}$ from posterior samples and report the equivalent Gaussian tension $T_\sigma$ (see \ref{['eqn:T']}). Combinations involving PP&SH0ES and/or BAOtr yield substantially reduced tension in $w_0w_a$CDM, while combinations with standard three-dimensional BAO (SDSS or DESI) remain in significant tension.
• Figure 3: Late-time expansion history reconstructed from each dataset combination in $\Lambda$CDM (left) and $w_0w_a$CDM (right). Top panels show the conformal Hubble rate $H(z)/(1+z)$; bottom panels show the deceleration parameter $q(z)$. Solid curves denote posterior means and shaded bands the $1\sigma$ credible regions. The horizontal dashed line marks the acceleration boundary $q=0$. The hatched region ($q<-1$) corresponds to super-acceleration ($\dot H>0$), i.e. $w_{\rm tot}<-1$ for the total cosmic fluid; in GR this implies $\rho_{\rm tot}+p_{\rm tot}<0$ (NEC violation by the total cosmic fluid in GR). The strong spread among reconstructions in the $w_0w_a$CDM case highlights the pronounced dataset dependence of CPL late-time dynamics.
• Figure 4: Correlations among the present-day CPL parameter $w_0$, the deceleration parameter $q_0$, and the matter density $\Omega_{\rm m}$ in the $w_0w_a$CDM model for the dataset combinations considered. Different late-time distance probes select distinct regions of this parameter space. In particular, the CMB-only CPL posterior allows an extended phantom-like tail ($w_0<-1$) that maps to $q_0\lesssim -1$ when combined with low $\Omega_{\rm m}$, reflecting the broad CMB geometric degeneracy in CPL. By contrast, CMB+DESI favors higher $\Omega_{\rm m}$ and a nearly coasting present-day expansion ($q_0\simeq 0$). Contours enclose 68% and 95% credible regions.
• Figure 5: Bayesian model comparison between $w_0w_a$CDM (CPL) and $\Lambda$CDM for each dataset combination. Bars show the evidence difference $\Delta\ln\mathcal{Z}\equiv \ln\mathcal{Z}(\mathrm{CPL})-\ln\mathcal{Z}(\Lambda\mathrm{CDM})$; $\Delta\ln\mathcal{Z}>0$ favors CPL. The revised Jeffreys' scale (Trotta) is overlaid to interpret the strength of evidence, as defined in the text. Strong-to-very-strong evidence in favor of CPL is obtained for combinations including PP&SH0ES and/or BAOtr, while CMB-only and CMB+DESI remain inconclusive; CMB+SDSS yields moderate evidence in favor of $\Lambda$CDM.