Realization of quintom dark energy after DESI DR2 in Nieh-Yan modified teleparallel gravity

Recent observations from the DESI Collaboration indicate a preference for quintom dark energy, i.e., its equation of state evolves across the cosmological constant boundary $w=-1$. It is well known that models with single perfect fluid or single scalar field minimally coupled to Einstein gravity develop perturbative instabilities around the crossing, thereby cannot realize the quintom scenario. In this paper, we propose a method to circumvent the instability problem of these models by considering the coupling of dark energy to the Nieh-Yan density within the framework of teleparallel gravity. We show that with this coupling the background evolution is not affected, but the dark energy perturbation is removed from the menu of dynamical degrees of freedom, thus avoiding the inherent difficulties in the old models. Furthermore, the Nieh-Yan coupling causes parity violation in gravitational waves, and this can be considered as a clear prediction of this mechanism.