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A Nieh-Yan coupling in teleparallel gravity erases the dark-energy perturbation at the w=-1 crossing, letting a single fluid or scalar realize quintom behavior without ghost or gradient instabilities, and predicting gravitational-wave biref

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2026-08-03 05:59 UTC pith:OGF7KRLU

load-bearing objection Clever new mechanism to kill quintom instabilities by constraining away the dark-energy perturbation, but the paper contradicts itself on whether the key constraint is independent. the 3 major comments →

arxiv 2602.00506 v3 pith:OGF7KRLU submitted 2026-01-31 gr-qc astro-ph.COhep-phhep-th

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

Yuxuan Kang , Mingzhe Li , Changzhi Yi This is my paper
classification gr-qc astro-ph.COhep-phhep-th
keywords quintom dark energyNieh-Yan modified teleparallel gravityw=-1 crossingdark energy perturbationsghost instabilitygradient instabilitygravitational wave birefringenceDESI DR2
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper addresses a known obstruction: single-component dark energy models that cross the cosmological-constant boundary w=-1 suffer unavoidable ghost or gradient instabilities in their perturbations. It proposes a way around this in Nieh-Yan modified teleparallel gravity, where dark energy couples to a topological torsion term. The coupling does not change the background Friedmann equations, but it generates a constraint that forces the gauge-invariant dark energy perturbation to vanish, deleting it from the set of dynamical fields. If correct, the quintom-B behavior preferred by recent baryon acoustic oscillation data can be realized by ordinary single-fluid or single-k-essence models, with the added prediction that left- and right-handed gravitational waves travel at different speeds.

Core claim

The central claim is that the Nieh-Yan density TλμνT~λμν vanishes on the FRW background, so a shift-symmetric coupling c/2 φ TλμνT~λμν does not feed back into background dynamics, but at first order the tetrad pseudoscalar perturbation λ enters the quadratic action only through S_NY^(2) = -∫ d⁴x a² [4c ∂i∂i λ (H δφ_1 + ψ φ'_1)]. Varying with respect to λ gives the constraint H δφ_1 + ψ φ'_1 = 0, which is exactly the vanishing of the gauge-invariant curvature perturbation ζ_1 for dark energy. After imposing this constraint, the quadratic scalar action reduces to that of the matter sector alone; the dark-energy perturbation is no longer dynamical, so the negative sound-speed and wrong-sign kin

What carries the argument

The central object is the Nieh-Yan density, the topological torsion invariant TλμνT~λμν = (1/2) εμνρσ Tλμν Tλρσ, coupled to dark energy with strength c. In the teleparallel formulation, the tetrad contains a pseudoscalar perturbation λ that does not appear in the metric. The coupling's quadratic action is linear in λ; since λ is non-dynamical, its equation of motion becomes the constraint H δφ_1 + ψ φ'_1 = 0, i.e. ζ_1 = 0. This constraint is the load-bearing device: it removes the dark-energy perturbation from the dynamical system, eliminating the ghost and gradient instabilities, while the Friedmann background is untouched because the Nieh-Yan density vanishes on the homogeneous, isotropic

Load-bearing premise

The result rests on treating the tetrad pseudoscalar perturbation λ as an independent auxiliary field, so that its equation of motion H δφ_1 + φ'_1 Ψ = 0 is a genuine constraint that eliminates the dark-energy perturbation; the paper itself notes that the antisymmetric field equation behind this constraint is not independent of the symmetric equation, so if λ is a gauge artifact of local Lorentz symmetry, the removal of ζ1 may be a gauge choice rather than a physical eliminat

What would settle it

Compute the exact quadratic Hamiltonian in a fixed physical gauge after integrating out λ; if the kinetic matrix for the remaining dark-energy and metric perturbations is positive definite, the dark-energy mode is genuinely absent, whereas a zero eigenvalue tied to local Lorentz gauge symmetry would mean the instability is merely hidden. A numerical lattice simulation of the full action crossing w=-1 would provide the same decisive test.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • In NYTG, a single perfect fluid whose equation of state follows the CPL form w0+wa(1-a) can cross w=-1 at z≈0.44 with no perturbative instability; only background equations need to be solved.
  • A single k-essence scalar with L = X + c1√X - V(φ) can also cross w=-1 smoothly in the constructed example, so the single-scalar no-go theorem is circumvented.
  • Dark energy perturbations vanish identically at linear order, so the dark-energy sector acts as a background-only component and matter perturbations obey a standard single-field action with a modified mass term.
  • Gravitational waves of opposite circular polarizations acquire different phase velocities, v_p ≈ 1 ± cφ'_1/k, a parity-violating signal that can be searched for in existing and future gravitational-wave data.
  • The bound from current binary black hole gravitational-wave events translates to |cφ'_1/a| < 3.25×10⁻⁴² GeV, giving a concrete target for future tests of the mechanism.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • An implication the paper leaves implicit is that dark energy becomes effectively non-clustering: without a dark-energy perturbation, observables such as the integrated Sachs-Wolfe effect and CMB lensing would resemble a matter-only universe with a modified background expansion; this could be tested against cosmological data.
  • The paper itself notes that the antisymmetric field equation (21) is not independent of (20), suggesting the constraint may be tied to the theory's local Lorentz redundancy. If λ is a pure-gauge mode, the removal of ζ1 might be a gauge choice rather than a physical elimination, and a fully gauge-invariant Hamiltonian analysis would be needed to confirm the instability is truly gone.
  • The same coupling could be applied beyond dark energy, for example to suppress isocurvature perturbations in multifield inflation or to freeze density perturbations of an extra component; these applications are not explored in the paper but follow directly from the constraint mechanism.
  • The paper's stability demonstration is limited to linear perturbation theory. At nonlinear order, auxiliary fields can develop kinetic terms once integrated out, so a numerical lattice simulation or full Hamiltonian analysis of the NYTG action across the crossing would test whether the healthy behavior persists beyond quadratic order.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a way to evade the quintom no-go theorem by coupling single-fluid or single-k-essence dark energy to the Nieh-Yan density in teleparallel gravity (NYTG). Because the Nieh-Yan density vanishes on the FRW background, the background dynamics are unchanged; at the perturbative level the tetrad pseudoscalar perturbation lambda enters linearly and, when integrated out, yields a constraint H*delta_phi1 + psi*phi1' = 0, i.e. zeta1 = 0. The authors then reduce the quadratic scalar actions to a single matter-sector variable, Eqs. (41) and (55), concluding that the dark-energy perturbation is removed from the dynamical spectrum and the instabilities of Section II are avoided. Two toy models are presented as quintom-B examples, and a parity-violating gravitational-wave birefringence prediction is derived. The paper is clearly written and the strategy is interesting, but the central mechanism relies on treating the above constraint as genuinely independent, which the manuscript itself does not reconcile with its earlier statement that Eq. (21) is not independent of Eq. (20).

Significance. If the central claim holds, the result is significant: it would allow a single perfect fluid or a single k-essence-like scalar to cross w = -1 while remaining perturbatively stable, without introducing additional dark-sector degrees of freedom, and it would make gravitational-wave parity violation a generic observational signature. The paper benefits from explicit reduced quadratic actions, use of the already-published NYTG framework, and a concrete falsifiable prediction. The limitation is that the main claim is exactly where the manuscript's own text creates ambiguity, so my assessment of significance is conditional on a rigorous demonstration of the constraint structure.

major comments (3)
  1. [Section III, Eq. (21); Section IV B2, Eq. (37)] The load-bearing step is treating H*delta_phi1 + psi*phi1' = 0 as an independent constraint that eliminates zeta1. But Section III states that Eq. (21), the antisymmetric field equation from which this perturbed constraint descends, 'is not independent of Eq. (20)'. If Eq. (37) is merely a combination of the other perturbed Einstein/fluid equations, it is not a new constraint; initial data for zeta1 remain free and the negative-c_s^2/ghost instabilities of Section II still propagate. The manuscript never reconciles this contradiction. Please provide an explicit count of independent scalar constraints and dynamical degrees of freedom at linear order, for example by solving the complete linearized system without imposing Eq. (37), or by a Dirac-Bergmann analysis. The reduced action (41), obtained after imposing (37), cannot by itself prove the reduction.
  2. [Section IV B2, Eq. (36); Section III] The derivation integrates out lambda because it appears linearly in S_NY. However, lambda is a tetrad perturbation that does not appear in the metric and is invariant under the listed diffeomorphisms, Eq. (29). Whether lambda is a physical auxiliary field or a pure-gauge remnant of the local Lorentz redundancy in the Weitzenbock gauge is crucial: if it is pure gauge, varying the quadratic action with respect to it may not generate a physical constraint. The paper should identify the residual local Lorentz transformation associated with lambda and show explicitly that the constraint H*delta_phi1 + psi*phi1' = 0 survives as an independent equation after that redundancy is fixed.
  3. [Sections IV and V, stability claims] All stability conclusions are based on the quadratic action at linear perturbation order. The abstract and conclusion claim that the dark-energy perturbation is 'removed from the menu of dynamical degrees of freedom', but no nonlinear Hamiltonian analysis is provided. Please either supply a nonlinear constraint/Hamiltonian analysis or explicitly state that the claim is limited to linear order. As it stands, the reader cannot tell whether the elimination of zeta1 is an exact property of the theory or an artifact of the quadratic truncation.
minor comments (4)
  1. [Section V B 1, after Eq. (50)] The sentence 'These equations are formally identical to those in Eqs. (50)' is a self-reference; it should refer to the corresponding scalar perturbation equations in Section IV, e.g. Eqs. (32), or to a different numbered set.
  2. [Throughout] Typographical issues: 'straitforwardly' in Section II, 'the the gauge-invariant' after Eq. (37), and 'Nieh-Ya n' in the title. Please proofread.
  3. [Section IV C and V C, Figs. 3 and 4] The CPL parameters in the fluid toy model are taken as the DESI best fit, while the scalar toy model parameters are simply chosen; please state in the captions or text that both are illustrative and not fits to data.
  4. [Eq. (42)] After eliminating zeta1, the matter-sector mass term still contains c_s1, which diverges at the crossing. A brief comment explaining why this does not reintroduce a problem would help, since a reader might otherwise worry about a divergent coefficient in the reduced action.

Circularity Check

0 steps flagged

No circular derivation; the central ζ1=0 result follows from varying the quadratic action and is not a fitted or self-referential input. Only minor non-load-bearing self-citations are present.

full rationale

The paper's central claim—that the Nieh-Yan coupling removes the dark-energy perturbation—is derived by a direct first-order calculation: the tetrad and matter perturbations are substituted into the action, the quadratic action (36) is obtained, and variation with respect to λ gives the constraint Hδφ1 + ψφ'1 = 0 (Eq. 37), which is equivalent to ζ1 = 0. Substituting this constraint into the quadratic action yields the reduced actions (41) and (55). No fitted parameter, observational input, or previously published result is used to obtain this constraint; DESI best-fit w0, wa enter only in the illustrative background toy models and are not used to predict the perturbation removal. The scalar-field toy model is also explicitly described as 'only an illustrative example.' Self-citations to [58,59] define the NYTG model and provide the local-Lorentz gauge discussion, but the relevant perturbation equations and quadratic actions are re-derived in this paper rather than imported as conclusions. A separate technical concern is the paper's statement that Eq. (21) is 'not independent of Eq. (20)' while later referring to its perturbed form as an 'additional constraint'; this is a consistency question about constraint counting, not a circular use of inputs or fits. Hence the circularity score is low, reflecting only minor self-citations that do not carry the derivation.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central mechanism requires only the Nieh-Yan coupling constant c and the perturbative constraint structure. The toy-model parameters (CPL w0,wa; scalar c1,Λφ,mφ,λφ and initial conditions) are illustrative inputs, not derived results. No new particles, forces, or dimensions are postulated.

free parameters (5)
  • c (Nieh-Yan coupling constant)
    Free coupling governing the strength of the dark-energy/Nieh-Yan interaction; unconstrained in the paper except by the GW bound |cφ'_1/a| < 3.25e-42 GeV.
  • w0, wa (CPL parameters) = w0=-0.667, wa=-1.09
    Taken from the DESI+CMB+Union3 best fit for the fluid toy model; not derived in the paper.
  • f0 (present dark energy density) = 8.63e-61
    Sets the overall dark energy scale in the fluid toy model; follows from the assumed Ωm0≈0.31 and h≈0.69.
  • Ωm0, h = 0.31, 0.69
    Assumed background cosmological parameters used to set the toy model evolutions.
  • Scalar toy model parameters (c1, Λφ, mφ, λφ, φ1ini, φdot1ini) = c1=-1.14e-60, Λφ=5.29e-121, mφ=1.12e-60, λφ=7.69e-121, φ1ini=0.6, φdot1ini=-8.06e-61
    Hand-picked to produce a quintom-B crossing at z≈0.44; labeled by the authors as illustrative.
axioms (5)
  • domain assumption The diagonal FRW tetrad with Weitzenböck gauge is valid, and the Nieh-Yan density vanishes on this background.
    Used in Sec. IV.A with tetrad (24); if the background had nonzero Nieh-Yan density, the background evolution would be modified.
  • domain assumption The no-go theorem for single-fluid and single-k-essence quintom is correctly captured by the quadratic actions (12) and (16).
    Sec. II relies on this to motivate the cure; adopted from Refs. [6,18-23].
  • domain assumption Linear perturbation theory around FRW is sufficient to establish physical stability.
    Secs. IV.B and V.B use truncated quadratic actions; no nonlinear or full Hamiltonian analysis is provided.
  • ad hoc to paper Eq. (21) can be used as an additional constraint even though the text states it is not independent of Eq. (20).
    Sec. III after Eq. (21) and Sec. IV.B.1 Eq. (31); the constraint-counting is not fully reconciled.
  • standard math Local Lorentz invariance permits the Weitzenböck gauge and identifies λ as a genuine non-propagating auxiliary field.
    Sec. III and Refs. [58,59]; this is the load-bearing structure for the ζ1=0 constraint.

pith-pipeline@v1.3.0-alltime-deepseek · 20299 in / 16832 out tokens · 191844 ms · 2026-08-03T05:59:57.751589+00:00 · methodology

0 comments
read the original 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 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.

Figures

Figures reproduced from arXiv: 2602.00506 by Changzhi Yi, Mingzhe Li, Yuxuan Kang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

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Forward citations

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Reference graph

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