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 DESI DR2, SDSS-IV, transverse/angular BAO (BAOtr), and Cepheid-calibrated PantheonPlus SN~Ia data. CPL inferences are strongly dataset-dependent. CMB data alone leave a broad geometric degeneracy, while DESI DR2 BAO pulls the reconstruction toward weak present-day acceleration. In contrast, CMB combined with PP\&SH0ES and BAOtr favors a moderately accelerating expansion and substantially reduces the Hubble tension. The origin of this behavior can be traced to low-redshift distance information: BAOtr and DESI/SDSS prefer different BAO distance ratios at $z\lesssim0.5$, which drives divergent CPL expansion histories. We quantify this mismatch directly at the data level by comparing angular BAO scales, including the common $z=0.510$ point and a conservative local interpolation of BAOtr with no extrapolation. Within CPL, where pre-recombination physics is fixed, $r_{\rm d}$ remains nearly unchanged, so shifts in $H_0$ are absorbed by late-time expansion freedom rather than by a change in the sound horizon. Bayesian evidence is likewise contingent on the low-redshift data: it favors CPL mainly when PP\&SH0ES and/or BAOtr are included, is inconclusive for CMB-only and CMB+DESI, and moderately favors $Λ$CDM for CMB+SDSS. These results show that apparent support for CPL and its ability to ease the Hubble tension are not universal, motivating more flexible late-time models and closer scrutiny of BAO systematics.