Unveiling the Pitfalls of CPL Parametrization at High Redshifts: A Critical Assessment of the $ω_{0}$$ω_a$CDM Model with DESI DR2 BAO Data

We critically assess the w0waCDM model, employing the Chevallier-Polarski-Linder (CPL) parametrization, against Baryon Acoustic Oscillation (BAO) measurements from DESI Data Release 2 (DR2). While DESI DR2 BAO observations are broadly consistent with a standard expansion history and matter density Omegam approximately 0.3, our Markov Chain Monte Carlo (MCMC) fits reveal observable-dependent shifts in best-fit parameters and degeneracy directions for the w0waCDM model, particularly when using rd-dependent and rd-independent observables separately. When constrained solely by DESI DR2 BAO data, the w0waCDM model exhibits a critical inconsistency: it predicts systematically lower values for DV/rd, DM/rd, and DH/rd, but higher values for the rd-independent ratio DM/DH. This tension arises from the inherent limitations of the CPL parametrization, particularly its behavior at high redshifts, where w(z) asymptotes to w0 + wa. To fit early-time observables like rd, the model is driven to high Omegam and large negative wa, resulting in parameter combinations that may lack physical plausibility. Our findings underscore that DESI DR2 BAO data alone is insufficient to constrain w0waCDM reliably, especially in the presence of CPL-induced degeneracies. Even ratio observables like DM/DH, which are independent of rd, are not immune to these effects. We advocate for constraining individual observables such as DV, DM, and DH separately--ideally combined with external priors on rd--to obtain more physically reliable constraints on evolving dark energy models. Ultimately, this study highlights the importance of caution when using approximate parametrizations such as CPL in precision cosmology, particularly across wide redshift ranges.