Revisiting CPL with sign-switching density: To cross or not to cross the NECB
Recent DESI DR2 BAO measurements, when combined with CMB and SNeIa data, exhibit a $3.2σ$-$3.4σ$ preference for dynamical dark energy (DE) described by the CPL-parametrized equation of state. A particularly striking feature of these reconstructions is an apparent transition from an early-time phantom-like regime to a late-time quintessence-like behavior. For positive-definite DE densities, this transition is often phrased as a crossing of the phantom divide line (PDL) at $w(a)=-1$. Allowing the DE density to become negative, however, renders the PDL (in the sense of $w(a)=-1$) non-diagnostic as a global separator: the physically meaningful criterion is instead the null energy condition boundary (NECB), $ρ_{\rm DE}+p_{\rm DE}=0$. We therefore test whether the data-driven preference for NECB-crossing in CPL reconstructions persists once alternative realizations of phantom behavior are admitted, specifically through sign-switching DE densities. To this end, we introduce and constrain two controlled phenomenological extensions of the CPL framework featuring a negative DE phase in the past. In the CPL$\to-Λ$ model, the switching epoch is tied to the CPL-inferred NECB-crossing scale factor, yielding an early-time negative cosmological-constant phase, while the post-switch evolution follows the CPL branch. In the sCPL model, the CPL equation of state is maintained at all times, while the sign switch in the energy density occurs at an independent transition redshift. We find that late-time BAO and SNeIa data drive the negative-density phase beyond their effective redshift coverage, and that this requirement is the primary driver of the inferred parameter behavior. While both models are statistically disfavored relative to the baseline CPL, admitting a negative DE phase generally reduces the significance of deviations from a cosmological constant.