Physical vs phantom dark energy after DESI: thawing quintessence in a curved background

Recent data from DESI, in combination with other data, provide moderate evidence of dynamical dark energy, $w\neq-1$. In the $w_0, w_a$ parametrization of $w$, there is a preference for a phantom crossing, $w<-1$, at redshift $z\sim0.5$. In general relativity, the phantom equation of state is unphysical. Thus it is important to check whether phantom crossing is present in other physically self-consistent models of dark energy that have equivalent evidence to the $w_0, w_a$ parametrization. We find that thawing quintessence with nonzero cosmic curvature can fit the recent data as well as $w_0, w_a$ in a flat background, based on both parametric and realistic scalar field evolutions. Although the realistic model does not allow $w<-1$, the parametrizations do allow it. However even if we allow $w<-1$ the data do not enforce phantom crossing. Thus, the phantom crossing is an artifact of a parametrization that is not based on a physical model.