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Type 3 New General Relativity has five stable propagating modes, matching the theory's Hamiltonian count.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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In New General Relativity on a flat expanding universe, the propagating spectrum is computed for all nine types, with Type 3 carrying five stable tensor, scalar, and vector modes.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection Type 3's five-mode claim rests on an invalid elimination of \tilde{V}_i, but the paper's vierbein framework and scalar/tensor sectors are solid enough to send back for revision. the 3 major comments →

arxiv 2509.18772 v2 pith:BSAR6JQS submitted 2025-09-23 gr-qc astro-ph.COhep-th

Cosmological Perturbation in New General Relativity: Propagating mode from the violation of local Lorentz invariance

Kyosuke Tomonari , Taishi Katsuragawa , Shin'ichi Nojiri This is my paper
classification gr-qc astro-ph.COhep-th MSC 83D0583F05 PACS 04.50.Kd98.80.Bp
keywords New General Relativitycosmological perturbationslocal Lorentz invariance violationvierbein perturbationteleparallel gravitypropagating modesFLRW spacetimeHamiltonian constraint analysis
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 reading

This paper asks which version of New General Relativity—a teleparallel theory of gravity with torsion—can describe perturbations of an expanding universe. Because local Lorentz invariance is broken in NGR (except in the teleparallel-equivalent-of-GR limit), the antisymmetric part of the vierbein field is not gauge and must be kept as physical. The authors rebuild the cosmological perturbation variables so that each one maps to a definite vierbein component, fix the spatially flat gauge, and compute second-order Lagrangians around flat FLRW spacetime for all nine NGR types. They find that Type 3 has exactly five stable propagating modes—tensor, scalar, and vector—in agreement with the five non-linear degrees of freedom from the canonical Hamiltonian count, making Type 3 the NGR type best suited for cosmological applications. They also show which other types gain modes and flag that Type 3's full usefulness still depends on avoiding strong couplings, left for future work.

Core claim

New General Relativity, when linearized around a flat expanding universe, contains extra gravitational degrees of freedom that appear only because local Lorentz symmetry is violated. The paper's main result is a mode-by-mode census: in the second-order Lagrangian, the tensor mode h_ij propagates in Types 1, 2, 3, 5, 6, and 8; the scalar α propagates in Type 3 and others; the pseudo-scalar σ̃ propagates in Types 1, 2, 4, 5, and 9; and the vector α_i or pseudo-vector Ṽ_i propagate in various types. In particular, Type 3 (parameter condition 2c1 + c2 = 0) yields five stable propagating modes—h_ij, α, and α_i—that coincide with the five non-linear degrees of freedom found by canonical constrain

What carries the argument

The carrying mechanism is the separation of the (co-)vierbein into a symmetric metric part and an antisymmetric part whose fields (α, σ̃, α_i, Ṽ_i) encode broken local Lorentz invariance. Alongside it, the spatially flat gauge—φ=0, B=0, C_i=0—is the gauge choice that keeps these antisymmetric fields physical instead of fixing them away. The propagation is decided by three parameter combinations, (2c1 − c2 + c3), (2c1 + c2), and (2c1 − c2), which appear as coefficients of the kinetic terms for the scalar, pseudo-scalar, vector, and pseudo-vector modes; their vanishing or sign selects which NGR type propagates which modes and whether the modes are ghost-free. For Type 3 the surviving fields a

Load-bearing premise

The whole argument rests on the canonical constraint result that local Lorentz invariance is broken in New General Relativity except in the teleparallel-equivalent-of-GR case; if that result is wrong, the antisymmetric vierbein fields are pure gauge and the new propagating modes are artifacts.

What would settle it

Redo the Type 3 perturbation theory around flat FLRW in a gauge that imposes both the diffeomorphism conditions and a local Lorentz condition that sets α=0 and α_i=0. If the reduced Lagrangian still shows only two propagating tensor modes, the five-mode result is a gauge artifact; if the reduced equations cannot be made consistent with the original dynamics, the perturbative counting is incomplete. A more observational check: the predicted scalar and vector modes would alter the relation between tensor and scalar cosmological perturbations, so measuring the polarization content of a gravitatio

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

If this is right

  • Type 3 NGR is ready to be used as a cosmological perturbation theory: its five modes (tensor, scalar, vector) line up with the five non-linear degrees of freedom, so no extra hidden constraints are expected at linear order.
  • The spatially flat gauge, with φ=0, B=0, C_i=0, is identified as the correct gauge for NGR-type theories; using other gauges that eliminate the antisymmetric vierbein fields can produce wrong mode counts.
  • Type 6 (teleparallel equivalent of GR) remains the only type with only tensor modes; every other regular NGR type gains at least one extra propagating mode from local Lorentz violation.
  • Type 3 has a ghost-free region of parameter space and preserves SO(3) spatial isotropy, making it consistent with a homogeneous and isotropic background while still modifying gravity.
  • Differences from earlier cosmological perturbation analyses in Types 4, 5, 7, and 8 are attributed by the authors to improper gauge choices in those earlier works, not just to higher-order terms.

Where Pith is reading between the lines

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

  • If Type 3 is healthy in the full non-linear theory, the extra scalar and vector modes could leave distinctive signatures in galaxy clustering, weak lensing, or gravitational-wave polarizations, giving a concrete way to distinguish NGR from general relativity.
  • The paper's gauge lesson generalizes beyond NGR: any cosmological perturbation calculation in theories with broken local Lorentz invariance that fixes away the antisymmetric vierbein fields will silently delete physical modes and should be treated with caution.
  • The matching between the canonical Hamiltonian count and the perturbative mode count for Type 3 suggests the theory may avoid strong coupling, but the paper explicitly leaves this verification open; a full non-linear analysis is the natural next step.
  • The same second-order Lagrangian machinery could be extended to higher-order or f(T)-type teleparallel models, where the pseudo-scalar and pseudo-vector sectors may behave differently.
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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 / 3 minor

Summary. The paper studies cosmological perturbations in New General Relativity (NGR) around a flat FLRW background, introducing a test scalar field as matter. It reviews the Dirac–Bergmann (DB) analysis of NGR, reconstructs the vierbein perturbation framework including the antisymmetric (local-Lorentz-violating) components, and derives the second-order Lagrangian for tensor, scalar, pseudo-scalar, and vector/pseudo-vector sectors. The central claim is that Type 3 NGR has five stable propagating modes (tensor h_ij, scalar α, vector α_i), matching the five nonlinear DOFs from the DB analysis, and is therefore preferable for cosmological applications (abstract, Table II). The paper also reports mode counts and ghost-free parameter conditions for all nine NGR types and compares with earlier work.

Significance. If the central claim is correct, the paper provides a consistent cosmological perturbation theory for NGR that captures the extra degrees of freedom arising from the violation of local Lorentz invariance. The identification of Type 3 as a stable theory with five propagating modes, if valid, is an important step toward phenomenological applications in cosmology. The paper is transparent in its derivations, uses Cadabra for the algebra, and provides explicit appendices with torsion components. The systematic comparison with previous results in Refs. [19,21,22] and the consistent treatment of the vierbein antisymmetric part are valuable assets. However, the mode-count claim for Type 3 hinges on a questionable elimination of the pseudo-vector field in the vector sector, which must be resolved before the main conclusion can be accepted.

major comments (3)
  1. [§V.D, Eq. (60)] The elimination of \tilde{V}_i in Types 3/8 is not a valid auxiliary-field reduction. Varying Eq. (59) with respect to \tilde{V}_i gives Eq. (60), which contains explicit time derivatives of \tilde{V}_i ('+12(2c_1-c_2+3c_3)a^3 H^2 \dot{\tilde{V}}_j') as well as \dot{H}\tilde{V}_j. Thus Eq. (60) is an equation of motion, not an algebraic constraint. Substituting it into Eq. (59) to obtain Eq. (61) is not a legitimate reduction of the action; it changes the phase-space structure and can alter the number of propagating modes. The conclusion that the vector mode α_i propagates in Types 3 and 8 rests directly on this substitution. A proper treatment (e.g., Hamiltonian analysis or retaining \tilde{V}_i as a dynamical variable with a kinetic term) is required to establish the five-mode count.
  2. [§V.D, Eq. (57)] The identical issue arises in the Type 2/9 analysis. Equation (57), obtained by varying Eq. (56) with respect to α_i, contains '−2(2c_2−c_3)a^2 ϵ^{ijk} ∂_j \dot{\tilde{V}}_k', i.e., a time derivative of \tilde{V}_k. Substituting Eq. (57) into Eq. (56) to obtain Eq. (58) is therefore not an algebraic elimination. Although the central Type 3 claim is the most affected, this undermines the reported mode counts for Types 2 and 9 as well.
  3. [Table II] The ghost-free condition listed for Types 3 and 8, '2c_1−c_2−c_3>0', appears inconsistent with Eq. (54), which gives the vector-mode condition as '2c_1−c_2+c_3>0'. Under the Type 3/8 condition 2c_1+c_2=0, these differ by the sign of c_3. Please clarify which condition is intended and, if the table is wrong, correct it. This also affects the claimed stability region for Type 3.
minor comments (3)
  1. [§III, Eq. (14)] The gauge transformation for α is listed as α′ = α − (1/a)ξ^0, while the text says 'Other perturbations, h_ij, G_i, α, and σ̃, do not change'. The list is internally inconsistent; please clarify whether α is gauge invariant or not, and correct the text accordingly.
  2. [§V.D, Eq. (49)] Several terms in Eq. (49) are written with mixed index placement on the Levi-Civita symbol (e.g., 'ϵ^{ijk} ∂_j \tilde{V}_k' vs 'ϵ_{ijk}') and the spatial metric δ_{ij} is not always explicitly used. Please standardize the notation to avoid ambiguity.
  3. [§V.D, Eq. (60)] Eq. (60) has a free index mismatch: the left-hand side is a vector with index i (or j after renaming), but the first term contains '\dot{\tilde{V}}_j' with index j. The index structure should be checked; the terms '12(2c_1−c_2+3c_3)a^3 H^2 \dot{\tilde{V}}_j' and '4(2c_1−c_2+3c_3)a^3 \dot{H}δ^{ij} \tilde{V}_j' suggest a possible typo in the placement of i/j.

Circularity Check

0 steps flagged

No significant circularity: Type 3's five-mode count is derived from the explicit quadratic action; self-cited Dirac-Bergmann results are used as a consistency check and upper bound, not as the source of the mode count.

full rationale

I walked the derivation chain. The headline result for Type 3 (h_ij, α, α_i) is obtained by explicit second-order expansion of L_NGR + L_matter around flat FLRW: tensor sector (Eq. 32), scalar sector (Eq. 40), vector/pseudo-vector sector (Eqs. 53, 59, 61). The mode count is not imposed by the Dirac-Bergmann analysis; it follows from which fields carry quadratic kinetic terms in those Lagrangians, with ghost-free conditions determined by coefficient signs. No parameter is fitted to any target observable. The self-cited DB analyses [15,16] are used (a) to justify not fixing antisymmetric vierbein components like α_i and \tilde V_i, (b) to supply Table I regularity and nonlinear-DOF counts, and (c) as an upper-bound consistency check (e.g., Type 5's 'either α_i or \tilde V_i' conclusion). These are independent Hamiltonian computations whose assumptions do not include the perturbative mode counts, so under the review rules they count as independent support rather than circularity. The agreement between the five perturbative modes and the five DB DOFs is a cross-check, not an input. The vector-sector reduction at Eqs. (60)-(61) is a potential technical flaw (\tilde V_i's Euler-Lagrange equation contains \dot{\tilde V}_j, so substituting it into the action is not an algebraic elimination), but a derivation error of this kind is not one of the enumerated circularity patterns; it is a correctness risk, not a self-referential reduction. No fitted-input-called-prediction, renaming, ansatz-smuggling, or uniqueness-imported-from-authors step was found. The self-citation reliance is substantial but not circular, so the score is 2.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

The central claim depends on: (1) the prior DB result that local LI is broken, (2) the standard quadratic-action mode-counting method, and (3) the FLRW background setup. The NGR parameters c1,c2,c3 are theory inputs, not fitted.

free parameters (1)
  • c1, c2, c3
    Intrinsic NGR coupling constants, not fitted in this work; all results are conditional on them.
axioms (3)
  • domain assumption Local Lorentz invariance is violated in NGR except Type 6 (TEGR), so the antisymmetric vierbein perturbations are physical and must not be gauged away.
    Invoked in Sec. II B (review of Refs. [15,16]) and Sec. III to justify the spatially flat gauge and the preservation of alpha, sigma_tilde, alpha_i, V_tilde_i.
  • domain assumption The flat FLRW background with a test scalar field satisfies the background equations, and the perturbative quadratic action around it determines the propagating modes.
    Sec. IV; for Types 5,8,9 the background is not determined (H arbitrary), yet mode counts are reported.
  • standard math Standard method: presence of a non-degenerate kinetic term in the reduced quadratic action after solving auxiliary constraints indicates a propagating mode.
    Used throughout Sec. V; questionable for the vector sector where constraints contain velocities.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Cosmological Perturbation in New General Relativity: Propagating mode from the violation of local Lorentz invariance." pith.science (2026). https://pith.science/paper/BSAR6JQS

@misc{pith2026250918772,
  author       = {Pith},
  title        = {Pith review of: Cosmological Perturbation in New General Relativity: Propagating mode from the violation of local Lorentz invariance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BSAR6JQS}},
  note         = {Machine review of arXiv:2509.18772}
}
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read the original abstract

We investigate the propagating modes of New General Relativity (NGR) in second-order linear perturbations in the Lagrangian density (first-order in field equations). The Dirac-Bergmann analysis has revealed a violation of local Lorentz invariance in NGR. We review the recent status of NGR, considering the results of its Dirac-Bergmann analysis. We then reconsider the vierbein perturbation framework and identify the origin of each perturbation field in the vierbein field components. This identification is mandatory for adequately fixing gauges while guaranteeing consistency with the invariance ensured by the Dirac-Bergmann analysis. We find that the spatially flat gauge is adequate for analyzing a theory with the violation of local Lorentz invariance. Based on the established vierbein perturbative framework, introducing a real scalar field as matter, we perform a second-order perturbative analysis of NGR with respect to tensor, scalar, pseudo-scalar, and vector and pseudo-vector modes. We reveal the possible propagating modes of each type of NGR. In particular, we find that Type 3 has stable five propagating modes, \textit{i.e.}, tensor, scalar, and vector modes, compared to five non-linear degrees of freedom, which results in its Dirac-Bergmann analysis; the linear perturbation theory of Type 3 is preferable for applications to cosmology. Finally, we discuss our results in comparison to previous related work and conclude this study.

discussion (0)

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Gauge-invariant cosmological perturbations in Type 3 New General Relativity and background-hierarchy bounds

    gr-qc 2026-05 unverdicted novelty 6.0

    Derives background-hierarchy bounds on the two free parameters of Type 3 NGR to ensure linear cosmological perturbation theory remains viable around flat FLRW.

  2. Gauge-invariant cosmological perturbations in Type 3 New General Relativity and background-hierarchy bounds

    gr-qc 2026-05 unverdicted novelty 5.0

    Derives background-hierarchy bounds for scalar, transverse-vector and tensor modes in Type 3 NGR around flat FLRW, identifying viable parameter regions where linear perturbation theory remains consistent.

  3. Vector modes in Type 3 New GR

    gr-qc 2026-05 unverdicted novelty 2.0

    Substituting constraint equations into the Lagrangian leads to false claims of dynamical vector modes in Type 3 New GR; analysis of the linear equations of motion confirms they are not dynamical.

  4. Vector modes in Type 3 New GR

    gr-qc 2026-05 unverdicted novelty 2.0

    Vector modes in Type 3 New GR are non-dynamical; substituting constraints into the Lagrangian produces incorrect claims of dynamics.

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.