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

TL;DR

This paper demonstrates that quintom dark energy, whose equation of state crosses the cosmological-constant boundary $w=-1$, can be realized without perturbative instabilities by coupling dark energy to the Nieh–Yan density in Nieh–Yan modified teleparallel gravity (NYTG). The key mechanism is that the Nieh–Yan coupling vanishes at the homogeneous FRW background, leaving background evolution unchanged, while imposing extra constraints at the perturbative level that remove the dark-energy perturbation as an independent dynamical degree of freedom. The authors analyze both a single perfect-fluid dark-energy model and a single k-essence-like scalar field within NYTG, showing that the perturbations become non-dynamical and that the usual gradient and ghost instabilities are avoided around $w=-1$ crossing. They construct explicit quintom-B realizations with toy background evolutions and a concrete scalar-field model, demonstrating crossing redshifts compatible with observations and illustrating a viable route for dynamical dark energy within a modified-gravity framework.

Abstract

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 provide a method to circumvent the instability problem of these models by introducing the coupling of dark energy to the Nieh-Yan density in 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 intrinsic difficulties in the old models.

Figures (5)

• Figure 1: The left panel illustrates the energy density $\rho(n)$ as a function of the particle number density $n$ in the quintom-B scenario. The right panel shows the $P-\rho$ relation in the same scenario. Arrows indicate the direction of evolution.
• Figure 2: The evolution of $w_{_{DE}}(z)$ of single fluid dark energy with $w_0=-0.67,\, w_a=-1.09$ and $f_0/M^2=3.96\times10^{-6}$. The gray dashed line marks the cosmological constant $\Lambda$ with EoS parameter $w=-1$.
• Figure 3: The way $w_{_{DE}}(z)$ changes with different values of a certain parameter. Left panel corresponds to different values of $w_0$ and right panel is associated with different values of $w_a$. The gray dashed line in both of panels marks the cosmological constant $\Lambda$ with EoS parameter $w=-1$.
• Figure 4: Left panel: evolution of EoS parameter $w_{_{DE}}(z)$ as a function of redshift $z$ and the gray dashed line marks the cosmological constant $\Lambda$ with EoS parameter $w=-1$. Right panel: the phase space trajectory of the solution with initial conditions $\dot{\phi}_{1_{ini}}/M=-1.06$ and $\phi_{1_{ini}}=0.7$.
• Figure 5: The way $w_{_{DE}}(z)$ changes with different values of a certain parameter. Upper left panel corresponds to different values of $c_1$ and upper right panel is associated with different values of $c_2/M$. Lower left panel is related to different values of $\Lambda_{\phi}/M^2$ and lower right panel is associated with different values of $m_{\phi}/M$. The gray dashed line shows the EoS parameter $w=-1$, which is corresponding to the cosmological constant $\Lambda$.