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

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.