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.

💡 Research Summary

The paper addresses a pressing issue raised by the latest DESI Data Release 2: observational analyses now show a 2.8–3.8 σ preference for dark‑energy equation‑of‑state (EoS) evolution that crosses the cosmological‑constant boundary w = –1, a behavior known as “quintom”. In standard General Relativity (GR) with a minimally coupled single perfect fluid or a single k‑essence‑type scalar field, such a crossing inevitably generates two fatal perturbative pathologies. First, the sound‑speed squared c_s² becomes negative around the crossing, producing a gradient instability that drives uncontrolled growth of fluctuations. Second, the kinetic coefficient z² changes sign, turning the perturbation into a ghost mode with unbounded Hamiltonian. These problems constitute a well‑known no‑go theorem for single‑component quintom models.

To circumvent these obstacles, the authors adopt the teleparallel equivalent of GR (TEGR), where gravity is encoded in torsion rather than curvature. Within this framework they introduce a coupling between the dark‑energy sector and the Nieh–Yan (NY) density, a topological invariant built from torsion. Crucially, the NY density vanishes identically on a homogeneous and isotropic Friedmann–Robertson–Walker (FRW) background, so the coupling does not modify the background Friedmann equations. The background evolution of the scale factor therefore remains identical to that of ΛCDM or any prescribed dynamical w(a) model.

The novelty lies in the perturbative sector. Varying the total action, which now contains an NY term of the form α φ N_Y, produces a constraint that forces the gauge‑invariant dark‑energy perturbation (denoted ζ₁ in the paper) to zero. In the quadratic action for scalar perturbations the usual two‑field structure (ζ₁, ζ₂) collapses to a single field (ζ₂, the matter perturbation). Consequently the dangerous coefficients c_s² and z² associated with the dark‑energy mode disappear, eliminating both gradient and ghost instabilities. The model thus achieves a stable w = –1 crossing with only a single dark‑energy component, without invoking extra fields, higher‑derivative operators, or non‑minimal couplings that typically plague quintom constructions.

To demonstrate viability, the authors present two toy models for the background EoS: (i) a linear CPL‑type parametrisation w(a)=w₀+w_a(1−a) and (ii) a logarithmic form w(a)=w₀+w₁ ln a. Both exhibit the “quintom‑B” behavior (transition from w > –1 to w < –1) favored by current data. Numerical integration shows that the background expansion matches observational constraints while the dark‑energy perturbation remains identically zero, confirming the theoretical expectation of stability.

An additional, experimentally testable prediction emerges from the NY coupling: it induces parity violation in the propagation of gravitational waves. The torsion‑based NY term contributes an antisymmetric piece to the graviton kinetic operator, leading to different dispersion relations for left‑ and right‑handed circular polarizations. This results in a birefringent effect—one polarization may be amplified while the other is damped—observable in future gravitational‑wave detectors (e.g., LISA, PTA networks, Cosmic Explorer). Detection of such parity‑violating signatures would provide a smoking‑gun test of the Nieh–Yan modified teleparallel gravity (NYTG) framework.

In summary, the paper proposes a theoretically clean and observationally testable mechanism to realize quintom dark energy: by coupling dark energy to the Nieh–Yan density within teleparallel gravity, the background dynamics are untouched, the problematic dark‑energy perturbation is eliminated, and a distinctive parity‑violating gravitational‑wave signal is generated. This approach sidesteps the traditional need for multiple fields or higher‑order derivatives, offering a minimalistic yet robust path to accommodate the DESI‑indicated quintom behavior. Future large‑scale structure surveys (DESI, Euclid, LSST) combined with precise gravitational‑wave polarization measurements will be crucial to confirm or falsify this intriguing proposal.