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REVIEW 3 major objections 4 minor 2 cited by

Weak Gravity Limit in Newer General Relativity

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Pith's one-line read STEGR with a determinant-gradient term has 1.5 new dynamical modes, not the 1 previously claimed.

desk verdict Careful weak-field analysis of Newer GR with a real correction to the mode count, but the extra half degree of freedom hangs on an interpretive choice about the flat connection, not on a first-principles derivation. read the letter →

arxiv 2501.00376 v3 pith:V7KJE6U7 submitted 2024-12-31 gr-qc hep-th

classification gr-qchep-th MSC 83D0583C25 PACS 04.20.-q04.50.Kd04.30.-w
keywords NewerGeneralRelativitysymmetricteleparallelgravityweaklimitdegreesoffreedomSTEGRnonmetricityunimodularflatconnection
verification ladder T0 review T1 audit T2 compute T3 formal

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 analyses the weak-field limit of Newer GR, the most general quadratic theory built from the nonmetricity tensor of a flat symmetric connection. It claims that requiring reasonable tensor and vector behavior fixes half of the parameter freedom, and that a previously accepted result is wrong: adding the square of the gradient of the metric determinant to STEGR produces one and a half new dynamical modes, not one. If true, the scalar sector of this model is not equivalent to GR plus one scalar field, and the extra half degree of freedom comes from the flat connection itself, which reduces the gauge group to volume-preserving coordinate changes. The result matters because the viability of modified teleparallel gravity depends on exactly how many degrees of freedom survive linearization.

What carries the argument

The load-bearing object is the flat symmetric connection in the coincident gauge, where connection coefficients vanish and partial derivatives of the metric play the role of nonmetricity. In the linearized scalar sector the decisive identity is chi equal to log of minus g, equation (40), which ties the would-be pure-gauge determinant mode to the preferred coordinates; together with the reduced linearised equations (35) through (37), this constraint leaves only volume-preserving coordinate changes as gauge and produces the extra half degree of freedom. The kinetic matrix and its principal-minor positivity analysis carry the no-ghost and no-full-dynamics result.

What would settle it

Perform a full Dirac-Bergmann constraint analysis of the model with a1 equal to a2, a4, and a5 but a3 different from a1, treating the flat connection components as independent variables; if the number of physical initial data per point is three rather than three and a half, the linearised counting is an artifact.

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Extended reading notes

Core claim

The paper's central claim is that the popular STEGR extension obtained by adding the square of the gradient of the metric determinant carries one and a half new dynamical degrees of freedom in its weak-field limit, not the single new mode attributed to it in the earlier literature. The counting is performed from the teleparallel viewpoint: the flat symmetric connection is an objective structure, so only coordinate changes with determinant equal to one are gauge once the field chi equal to log of minus the metric determinant is fixed. That reduces the kinematical gauge group from four diffeomorphism freedoms to three, and the remaining combination becomes a half-dynamical mode on top of the single scalar from chi. The paper also establishes that a fully dynamical, ghost-free Newer GR model is impossible and that in the linearized theory only the parameter combinations a1, a2 minus a4, a3, and a5 matter.

Load-bearing premise

The whole argument rests on treating the flat connection and its coincident-gauge coordinates as physical structure, so that only determinant-one coordinate changes count as gauge; drop that assumption and the extra half mode disappears.

Editorial extensions

If this is right

  • If the central claim is right, the STEGR plus determinant-gradient model must be treated as a three-and-a-half-degree-of-freedom theory in every subsequent application, including cosmology and gravitational-wave analysis.
  • The linearized theory depends on only four parameter combinations, with a2 and a4 entering only through their difference, so any observational distinction between those two coefficients must come from nonlinear effects.
  • A fully dynamical ghost-free Newer GR model is impossible, so a healthy theory must leave some metric components constrained exactly as in GR.
  • Within the viable scalar sector, deviations controlled by a3 or a5 both produce half-integer numbers of new modes, so the two deformations are not distinguished by the mode count alone.
  • Setting a1 to zero removes the standard tensor gravitational-wave polarisations, making such models unsuitable as theories of gravity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the flat connection really carries a half degree, viable Newer GR models should exhibit a scalar or preferred-frame gravitational signature controlled by the determinant-gradient term; computing that observable would be a natural next step beyond this paper.
  • Editorial inference: the same determinant-condition mechanism should apply to any symmetric-teleparallel action that breaks diffeomorphisms only through the metric determinant, so half-integer mode counts may be generic in that class.
  • Editorial inference: a full nonlinear Hamiltonian analysis of the a5-modified model would test whether the linearised half mode survives away from Minkowski spacetime or is removed by strong-coupling constraints.
  • Editorial inference: comparing scalar propagation speeds in the a3- and a5-modified models against gravitational-wave or pulsar-timing observations could distinguish the two viable deformations, which are degenerate in the mode count alone.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies the linearised weak-field limit of Newer GR, the most general parity-even quadratic action in the nonmetricity tensor (action (3)). It parametrises metric perturbations into scalar, vector, and tensor sectors, derives the linearised equations (22)-(25), and uses them to constrain the parameter space and count degrees of freedom. The central claim, stated in the abstract and Section 7.1, is that the STEGR-plus-(gradient of the metric determinant)² model has one and a half new dynamical scalar modes rather than one as previously claimed in Ref. [40], provided the flat connection is treated as an objective physical structure so that only volume-preserving coordinate changes are gauge (Eq. (40), χ = ln(−g)).

Significance. If the mode count is accepted, the paper corrects a previous result and maps out the viable parameter region of Newer GR in a transparent way. Its strengths are that the linearised equations, the kinetic matrix (17), and its determinant (18) are given explicitly, making the algebraic core checkable, and that the comparison with Ref. [40] is addressed directly. The main claim, however, is conditional on an interpretive assumption about the flat connection, and the paper does not provide an independent first-principles count that would settle whether the extra half mode is physical.

major comments (3)
  1. [Section 7.1, Eq. (40)] The claim of one and a half new modes is not derived from the action (3) alone; it presupposes that the flat connection is an objective physical field, so that only volume-preserving coordinate changes (det ∂ζ/∂x = 1) are gauge and χ = ln(−g) is a constraint. In the standard covariant symmetric-teleparallel formulation, the flat connection is a pure-gauge variable and the same linearised system reduces to the one-mode count of Ref. [40]. Since the paper does not give an independent first-principles count (for example, a covariant Hamiltonian or symplectic analysis) that selects the objective-connection interpretation, the headline three-halves claim remains conditional. The authors should either supply such a count or explicitly present the result as specific to the coincident-gauge teleparallel interpretation rather than as a definitive correction.
  2. [Section 7.1, after Eq. (39)] The text first says that the previous claim [40] 'is wrong' and then says 'we do agree with the scalar-tensor representation' and 'their analysis is also correct.' These statements are compatible only under the interpretive assumption discussed above; without it, Ref. [40]'s one-mode count is the correct result in the covariant formulation. The authors should remove the apparent contradiction by stating that the two counts apply to different frameworks, and by not calling the earlier count wrong without specifying that the disagreement concerns the physical status of the flat connection.
  3. [Section 3 and Section 7] The derivations repeatedly use the rule that an equation of the form Δ f = 0 is solved as f = 0, effectively treating Δ as an invertible operator and discarding harmonic and constant modes. Since the degree-of-freedom count in Section 7 depends on the number of initial data in this perturbative system, the authors should justify why the discarded modes cannot alter the count, or state explicitly that the result concerns only local modes with non-zero spatial momentum.
minor comments (4)
  1. [Abstract and Section 7.1] The phrase 'three halves new dynamical modes' is unusual; 'one and a half new dynamical degrees of freedom' would be less ambiguous, especially because the paper also speaks of 'three halves constrained and three halves dynamical modes.'
  2. [Eq. (17)] The grouping of fields in the kinetic matrix is indicated with braces in a way that is difficult to read; a table listing the fields and the corresponding blocks would improve clarity.
  3. [Section 7.1] The variable χ = ln(−g) is introduced both as a field and as a condition (40); the paper should state explicitly that this is an identity for the metric determinant rather than an independent constraint imposed by hand.
  4. [Footnote in Section 7.1] The remark about the notation in Ref. [40] being 'strange' is not needed for the technical argument and could be moved to a separate remark or omitted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 1.5-mode count is an explicit linearized calculation under a stated teleparallel gauge interpretation.

full rationale

The linearized analysis is self-contained: the quadratic action (3) is expanded around Minkowski in Section 3, the scalar equations (22)-(25) are derived explicitly from the linearized tensor (15), and the special case a1 = tilde-a2 = a5 with a3 != a1 is reduced in Section 7.1 to the system (39), from which the count of three scalar initial data (one for V and two for the phi/psi combination) follows by direct algebra. The comparison with Ref. [40] is an external benchmark: the paper reproduces the scalar-tensor equation square-chi = lambda0 e^{chi/2} and then disagrees only about whether the residual volume-preserving coordinate freedom should be counted as a gauge symmetry. That disagreement rests on the explicitly stated teleparallel interpretation, 'As long as we take the flat connection as something objective and sensical,' which is a physical assumption, not a hidden circular input. Self-citations to the authors' previous New GR papers and to Ref. [7] are methodological or geometric background and do not supply the degree-of-freedom count; no fitted parameter is renamed as a prediction, and no uniqueness theorem is imported to forbid alternatives. The claim is therefore conditional on the teleparallel viewpoint, but it is not circular.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no data fits and no new entities. The free parameters are the five Lagrangian coefficients, effectively four after the a2 - a4 degeneracy. The degree-of-freedom count rests on standard perturbation theory plus the interpretive assumption that the flat connection is physical.

free parameters (5)
  • a1
    Coefficient of Q_alpha_mu_nu Q^alpha_mu_nu in action (3). It sets tensor-mode dynamics and is scanned over, not fitted.
  • a2
    Coefficient of Q_alpha_mu_nu Q^mu_alpha_nu. In the weak-field limit it only enters through a_tilde2 = a2 - a4 because of the linearized degeneracy with a4 (Section 3.1).
  • a3
    Coefficient of Q_mu Q^mu. After stability constraints, it remains as one of two scalar-sector parameters; the a3-modification is the unimodular-like case in Section 7.1.
  • a4
    Coefficient of Q_tilde_mu Q_tilde^mu. Degenerate with a2 at linear order, so only the combination a_tilde2 = a2 - a4 matters.
  • a5
    Coefficient of Q_mu Q_tilde^mu. One of the two remaining scalar-sector parameters and the focus of the STEGR-plus-gradient-squared model.
assumptions (5)
  • domain assumption A global coincident gauge exists for the flat symmetric connection, so Q_alpha_mu_nu = partial_alpha g_mu_nu (Section 2, Eq. (1)).
    This is the defining setup of symmetric teleparallel gravity and is inherited from prior literature [3,7].
  • ad hoc to paper Equations of the form Delta f = 0 are solved as f = 0, and Delta is treated as a nonzero number in perturbation theory (Sections 3 and 5).
    The authors explicitly adopt this convention. It excludes harmonic and global modes and is standard in cosmological perturbation theory, but it is a choice that affects the degree-of-freedom count.
  • domain assumption The flat connection is objective and physical, so only volume-preserving diffeomorphisms are gauge, enforced by chi = ln(-g) in the coincident gauge (Section 7.1, Eq. (40)).
    This is the load-bearing premise for the extra half degree of freedom. In a fully covariant treatment with full diffeomorphism invariance, the prior count of one new mode is recovered.
  • standard math Sylvester's criterion characterizes positive definiteness of the kinetic matrix K (Section 4, Eq. (17)).
    Used to prove that a fully dynamical ghost-free Newer GR model is impossible.
  • domain assumption The action (3) is the most general parity-preserving quadratic Newer GR action, taken from Ref. [3].
    The analysis starts from this action and does not re-derive its uniqueness.

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Cite this review

Pith. "Pith review of Weak Gravity Limit in Newer General Relativity." pith.science (2026). https://pith.science/paper/V7KJE6U7

@misc{pith2026250100376,
  author       = {Pith},
  title        = {Pith review of: Weak Gravity Limit in Newer General Relativity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V7KJE6U7}},
  note         = {Machine review of arXiv:2501.00376}
}
read the original abstract

We analyse linearised field equations around the Minkowski metric with its standard flat parallel transport in models of Newer GR, that is quadratic actions in terms of nonmetricity tensor. We show that half of the freedom in choosing the model parameters is immediately fixed by asking for reasonable properties of tensors and vectors, defined with respect to spatial rotations, and accurately describe the much more complicated sector of scalars. In particular, we show that, from the teleparallel viewpoint, the model of STEGR with addition of a gradient squared of the metric determinant exhibits three halves new dynamical modes, and not just one like it was previously claimed.

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Forward citations

Cited by 2 Pith papers

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Reference graph

Works this paper leans on

46 extracted references · 5 canonical work pages · cited by 2 Pith papers

  1. [40]

    Bello-Morales, J

    A.G. Bello-Morales, J. Beltran Jimenez, A. Jimenez Cano, A.L. Mar oto, T.S. Koivisto. A class of ghost-free theories in symmetric teleparallel geometry . arXiv:2406.19355

  2. [1]

    Bahamonde, K.F

    S. Bahamonde, K.F. Dialektopoulos, C. Escamilla-Rivera, G. Farru gia, V. Gakis, M. Hendry, M. Hohmann, J. Levi Said, J. Mifsud, E. Di Valentino. Teleparallel Gravity: From Theory to Cosmology . Reports on Progress in Physics 86 (2023) 026901; arXiv:2106.13793

  3. [2]

    Nester, H.J

    J.M. Nester, H.J. Yo. Symmetric teleparallel general relativity . Chinese Journal of Physics 37 (1999) 113; arXiv:gr-qc/9809049

  4. [3]

    Beltran Jimenez, L

    J. Beltran Jimenez, L. Heisenberg, T.S. Koivisto. Coincident General Relativity . Physical Review D 98 (2018) 044048; arXiv:1710.03116

  5. [4]

    Beltran Jimenez, L

    J. Beltran Jimenez, L. Heisenberg, T.S. Koivisto. The Geometrical Trinity of Gravity . Universe 5 (2019) 173; arXiv:1903.06830

  6. [5]

    Golovnev

    A. Golovnev. Is there any Trinity of Gravity, to start with? arXiv:2411.14089 13

  7. [6]

    Golovnev

    A. Golovnev. The geometrical meaning of the Weitzenboeck connection . International Journal of Geometric Methods in Modern Physics 20 (2023) 2350219; arXiv:2302.13599

  8. [7]

    Blixt, A

    D. Blixt, A. Golovnev, M.J. Guzman, R. Maksyutov. Geometry and covariance of symmetric teleparallel theories of gravity . Physical Review D 109 (2024) 044061; arXiv:2306.09289

Show all 46 references
  1. [8]

    Ferraro, F

    R. Ferraro, F. Fiorini. Modified teleparallel gravity: inflation without inflaton . Physical Review D 75 (2007) 084031; arXiv:gr-qc/0610067

  2. [9]

    Bahamonde, Ch.G

    S. Bahamonde, Ch.G. Boehmer, M. Wright. Modified teleparallel theories of gravity . Physical Review D 92 (2015) 104042; arXiv:1508.05120

  3. [10]

    Hayashi, T

    K. Hayashi, T. Shirafuji. New general relativity . Physical Review D 19 (1979) 3524

  4. [11]

    M. Adak. The symmetric teleparallel gravity . Turkish Journal of Physics 30 (2006) 379; arXiv:gr-qc/0611077

  5. [12]

    Capozziello, M

    S. Capozziello, M. Capriolo, G. Lambiase. Gravitational tensor and scalar modes in f (Q,B ) non-metric gravity. Physical Review D 110 (2024) 104028; arXiv:2407.14862

  6. [13]

    Capozziello, M

    S. Capozziello, M. Capriolo. Gravitational waves in f (Q) non-metric gravity without gauge fixing . Physics of the Dark Unierse 45 (2024) 101548; arXiv:2405.16163

  7. [14]

    Capozziello, S

    S. Capozziello, S. Cesare, C. Ferrara. Extended Geometric Trinity of Gravity . arXiv:2503.08167

  8. [15]

    Guzman, L

    M.J. Guzman, L. Jarv, L. Pati. Exploring the stability of f (Q) cosmology near general relativity limit with different connections . Physical Review D 110 (2024) 124013; arXiv:2406.11621

  9. [16]

    Paliathanasis

    A. Paliathanasis. Testing Non-Coincident f (Q)-gravity with DESI DR2 BAO and GRBs . arXiv:2504.11132

  10. [17]

    Beltran Jimenez, T.S

    J. Beltran Jimenez, T.S. Koivisto. Lost in translation: the Abelian affine connection (in the coi ncident gauge) . International Journal of Geometric Methods in Modern Physics 19 (2022) 2250108; arXiv:2202.01701

  11. [18]

    Golovnev, M.J

    A. Golovnev, M.J. Guzman. Foundational issues in f(T) gravity theory . International Journal of Geometric Methods in Modern Physics 18 (2021) 2140007; arXiv:2012.14408

  12. [19]

    Golovnev

    A. Golovnev. Degrees of Freedom in modified Teleparallel Gravity . Ukrainian Journal of Physics 69 (2024) 456; arXiv:2405.14184

  13. [20]

    M. Li, R.X. Miao, Y.G. Miao. Degrees of freedom of f(T) gravity . Journal of High Energy Physics JHEP07(2011)108; arXiv:1105.5934

  14. [21]

    Ferraro, M.J

    R. Ferraro, M.J. Guzman. Hamiltonian formalism for f(T) gravity . Physical Review D 97 (2018) 104028; arXiv:1802.02130

  15. [22]

    Blagojevic, J.M

    M. Blagojevic, J.M. Nester. Local symmetries and physical degrees of freedom in f(T) gra vity: a Dirac Hamil- tonian constraint analysis . Physical Review D 102 (2020) 064025; arXiv:2006.15303

  16. [23]

    Tomonari, D

    K. Tomonari, D. Blixt. Degrees of Freedom of New General Relativity: Type 2, Type 3, Type 5, and Type 8 . arXiv:2410.15056

  17. [24]

    Tomonari

    K. Tomonari. Degrees of Freedom of New General Relativity 2: Type 4, Type 7 , and Type 9 . arXiv:2411.11118

  18. [25]

    Golovnev, A.N

    A. Golovnev, A.N. Semenova, V.P. Vandeev. Gravitational Waves in New General Relativity . Journal of Cosmology and Astroparticle Physics JCAP01(2024)003; arXiv:230 9.02853

  19. [26]

    Golovnev, A.N

    A. Golovnev, A.N. Semenova, V.P. Vandeev. Conformal Transformations and Cosmological Perturbation s in New General Relativity. Journal of Cosmology and Astroparticle Physics, JCAP04(2024) 064; arXiv:2312.16021

  20. [27]

    Blixt, M

    D. Blixt, M. Hohmann, Ch. Pfeifer. Hamiltonian and primary constraints of new general relativ ity. Physical Review D 99 (2019) 084025; arXiv:1811.11137

  21. [28]

    Guzman, Sh.K

    M.J. Guzman, Sh.K. Ibraheem. Classification of primary constraints for new general relat ivity in the premetric approach. International Journal of Geometric Methods in Modern Physics 1 8 (2021) 2140003; arXiv:2009.13430

  22. [29]

    D’Ambrosio,L

    F. D’Ambrosio,L. Heisenberg, S. Zentarra. Hamiltonian Analysis of f(Q) Gravity and the Failure of the Dirac-Bergmann Algorithm for Teleparallel Theories of Gra vity. Fortschritte der Physik 71 (2023) 2300185; arXiv:2308.02250 14

  23. [30]

    Hohmann, Ch

    M. Hohmann, Ch. Pfeifer, J. Levi Said, U. Ualikhanova. Propagation of gravitational waves in symmetric teleparallel gravity theories . Physical Review D 99 (2019) 024009; arXiv:1808.02894

  24. [31]

    D’Ambrosio, L

    F. D’Ambrosio, L. Heisenberg. Classification of Primary Constraints of Quadratic Non-Met ricity Theories of Gravity. Journal of High Energy Physics JHEP02(2021)170; arXiv:2007.05 064

  25. [32]

    Bajardi, D

    F. Bajardi, D. Blixt. Primary constraints in general teleparallel quadratic gra vity. Physical Review D 109 (2024) 084078; arXiv:2401.11591

  26. [33]

    Bajardi, D

    F. Bajardi, D. Blixt, S. Capozziello. The Hamilton equations in f(T) teleparallel gravity and in N ew General Relativity. arXiv:2412.20592

  27. [34]

    D. Zhao. Linear perturbations of symmetric teleparallel gravity on Minkowski background. arXiv:2412.20696

  28. [35]

    Mukhanov, H.A

    V.F. Mukhanov, H.A. Feldman, R.H. Brandenberger. Theory of cosmological perturbations . Physics Reports 215 (1992) 203

  29. [36]

    Golovnev

    A. Golovnev. On the degrees of freedom count on singular phase space subma nifolds. International Journal of Theoretical Physics 63 (2024) 212; arXiv:2311.10690

  30. [37]

    Hohmann, V

    M. Hohmann, V. Karanasou. Symmetric Teleparallel Connection and Spherical Solution s in Newer GR . arXiv:2412.11730

  31. [38]

    H.J. Yo, J.M. Nester. Hamiltonian analysis of Poincare gauge theory scalar modes . International Journal of Modern Physics D 8 (1999) 459; arXiv:gr-qc/9902032

  32. [39]

    Bahamonde, D

    S. Bahamonde, D. Blixt, K.F. Dialektopoulos, A. Hell. Revisiting Stability in New General Relativity . arXiv:2404.02972

  33. [41]

    Bello-Morales, A.L

    A.G. Bello-Morales, A.L. Maroto. Cosmology in gravity models with broken diffeomorphisms . Physical Review D 109 (2024) 043506; arXiv:2308.00635

  34. [42]

    Deffayet, Sh

    C. Deffayet, Sh. Mukohyama, A. Vikman. Ghosts without runaway . Physical Review Letters 128 (2022) 041301; arXiv:2108.06294

  35. [43]

    Deffayet, A

    C. Deffayet, A. Held, Sh. Mukohyama, A. Vikman. Global and Local Stability for Ghosts Coupled to Positive En - ergy Degrees of Freedom. Journal of Cosmology and Astroparticle Physics JCAP11(2023)0 31; arXiv:2305.09631

  36. [44]

    Errasti Diez, J

    V. Errasti Diez, J. Gaset Rifa, G. Staudt. Foundations of ghost stability . arXiv:2408.16832

  37. [45]

    Deffayet, A

    C. Deffayet, A. Held, Sh. Mukohyama, A. Vikman. Ghostly interactions in (1+1) dimensional classical field theory. arXiv:2504.11437

  38. [46]

    Aguiar Gomes, J

    D. Aguiar Gomes, J. Beltran Jimenez, T.S. Koivisto. Energy and entropy in the Geometrical Trinity of gravity . Physical Review D 107 (2023) 024044; arXiv:2205.09716 15

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