Dark Energy Crosses the Line: Quantifying and Testing the Evidence for Phantom Crossing

Abstract: Combinations of the most recent CMB, BAO, and SNeIa datasets, when analyzed using the CPL parametrization, $w(a) = w_0 + (1 - a) w_a$, exclude $\Lambda$CDM at $\gtrsim!3\sigma$ in favor of a dark energy equation of state (EoS) parameter that crosses the phantom divide. We confirm this behavior and show that it persists when DESI BAO data are replaced by SH0ES $H_0$ measurements, despite the known tension between these probes in the presence of CMB data. In both cases, the constraints favor a transition from an early-time phantom-like phase to a late-time quintessence-like phase, with the crossing occurring at different redshifts depending on the dataset combination. The probability that a phantom divide line (PDL) crossing does not occur within the expansion history is excluded at significance levels ranging between $3.1\sigma$-$5.2\sigma$. To investigate whether the apparent PDL crossing is a genuine feature preferred by the data or an artifact of the linear form of the CPL parametrization, we isolate the PDL crossing feature by introducing two modified versions of CPL that explicitly forbid it: CPL${}{>a\mathrm{c}}$ and CPL${}{<a\mathrm{c}}$. These models are physically motivated in that they phenomenologically capture the behavior of thawing and freezing scalar field scenarios. While previous studies have primarily considered thawing quintessence as a non-crossing alternative, we find that a freezing phantom-like model is the only one capable of performing comparably to CPL -- and only in a few cases. Nevertheless, across all dataset combinations considered, the standard CPL model consistently provides the best fit, strongly indicating that the data genuinely favor a PDL crossing.