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arxiv: 2606.30036 · v1 · pith:TBFEQX5Hnew · submitted 2026-06-29 · 🌀 gr-qc · astro-ph.CO

Physical nonviability of f(mathbb{Q}) in the scalar-tensor representation

Jose Beltr\'an Jim\'enez , Alejandro Jim\'enez Cano , Tomi S. Koivisto This is my paper

Pith reviewed 2026-06-30 05:25 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO
keywords f(Q) gravityscalar-tensor representationpathologiesmodified gravitynon-metricityinstabilitiesgeneral relativity alternatives
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0 comments X

The pith

f(Q) gravity exhibits pathological behavior when expressed in scalar-tensor form.

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

The paper establishes that f(Q) gravity, formulated using the non-metricity scalar, displays known physical pathologies once rewritten in its scalar-tensor representation. These pathologies involve unphysical degrees of freedom or instabilities that render the theory nonviable. A reader would care because f(Q) theories have been explored as alternatives to general relativity for late-time acceleration, yet the representation uncovers inconsistencies that prevent consistent physical use. The work confirms these issues through the equivalent scalar-tensor description.

Core claim

We show the known pathological character of f(Q) gravity in its scalar-tensor representation.

What carries the argument

The scalar-tensor representation of f(Q) gravity, which recasts the theory to expose its degrees of freedom and stability issues.

If this is right

  • f(Q) models cannot serve as consistent alternatives to general relativity without resolving the revealed instabilities.
  • Cosmological applications of f(Q) gravity must incorporate additional mechanisms to eliminate the pathological modes.
  • The nonviability extends to any physical predictions derived from the scalar-tensor equivalent form.

Where Pith is reading between the lines

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

  • Similar pathologies may appear in other non-metricity-based modified gravity theories when cast into scalar-tensor language.
  • Testing the theory against solar-system constraints could further highlight the instabilities identified in the representation.
  • Alternative formulations of f(Q) that avoid the scalar-tensor map might evade the issues but would require separate viability checks.

Load-bearing premise

The scalar-tensor representation faithfully captures all physical degrees of freedom and stability properties of the original f(Q) theory.

What would settle it

A calculation showing that the original f(Q) action yields stable dynamics without extra ghostly modes or instabilities when the scalar-tensor map is applied would falsify the claim.

read the original abstract

We show the known pathological character of $f(\mathbb{Q})$ gravity in its scalar-tensor representation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript claims to demonstrate the known pathological character of f(Q) gravity by examining its scalar-tensor representation, asserting that this form reveals physical nonviability.

Significance. If the scalar-tensor representation is shown to be dynamically equivalent without introducing artifacts and the pathologies are rigorously derived, the result would strengthen existing concerns about f(Q) theories in modified gravity and help delineate their limitations. No machine-checked proofs or parameter-free derivations are evident from the provided abstract.

major comments (1)
  1. [Abstract] The central claim requires dynamical equivalence between the scalar-tensor form and the original f(Q) theory, including preservation of all degrees of freedom and stability properties. The abstract frames the result as revealing the 'known pathological character' but provides no equations, derivations, or discussion of whether the auxiliary scalar or transformations alter the constraint structure or propagating modes (e.g., relaxing torsion-free conditions). This equivalence is load-bearing for the conclusion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their report and the opportunity to clarify our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] The central claim requires dynamical equivalence between the scalar-tensor form and the original f(Q) theory, including preservation of all degrees of freedom and stability properties. The abstract frames the result as revealing the 'known pathological character' but provides no equations, derivations, or discussion of whether the auxiliary scalar or transformations alter the constraint structure or propagating modes (e.g., relaxing torsion-free conditions). This equivalence is load-bearing for the conclusion.

    Authors: We agree that dynamical equivalence is essential. The scalar-tensor representation is obtained from f(Q) via the standard Legendre transform introducing an auxiliary scalar, which by construction preserves the original degrees of freedom, constraint structure, and torsion-free condition without introducing artifacts or new propagating modes. These steps and the resulting pathologies are derived explicitly in the body of the manuscript. We will revise the abstract to state this equivalence more clearly. revision: yes

Circularity Check

0 steps flagged

No circularity: demonstration of known pathology

full rationale

The paper's central claim is a demonstration that the scalar-tensor representation of f(Q) exhibits known pathologies. No derivation chain, equations, or self-citations are provided in the abstract that reduce a result to its own inputs by construction. The framing treats the pathology as pre-existing rather than newly predicted or fitted, and the equivalence assumption is presented as a premise rather than derived within the work. This is the most common honest non-finding for short demonstration papers.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, axioms, or invented entities; ledger left empty.

pith-pipeline@v0.9.1-grok · 5541 in / 906 out tokens · 33458 ms · 2026-06-30T05:25:28.360535+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

28 extracted references · 26 canonical work pages · 9 internal anchors

  1. [1]

    The Geometrical Trinity of Gravity

    J. Beltr´ an Jim´ enez, L. Heisenberg, and T. S. Koivisto, Universe5, 173 (2019), arXiv:1903.06830 [hep-th]. 6 We have in mind generic couplings. Of course one could always cure the instabilities by e.g. introducing a coupling to a matter field that happens to be a Lagrangian multiplier freezing the problematic as in the TDiff-invariant version discussed above

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  2. [2]

    Beltr´ an Jim´ enez, L

    J. Beltr´ an Jim´ enez, L. Heisenberg, D. Iosifidis, A. Jim´ enez-Cano, and T. S. Koivisto, Phys. Lett. B805, 135422 (2020), arXiv:1909.09045 [gr-qc]

    work page arXiv 2020

  3. [3]

    J. M. Nester and H.-J. Yo, Chin. J. Phys.37, 113 (1999), arXiv:gr-qc/9809049

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  4. [4]

    M. Adak, M. Kalay, and O. Sert, Int. J. Mod. Phys. D 15, 619 (2006), arXiv:gr-qc/0505025

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  5. [5]

    Coincident General Relativity

    J. Beltr´ an Jim´ enez, L. Heisenberg, and T. Koivisto, 6 Phys. Rev. D98, 044048 (2018), arXiv:1710.03116 [gr- qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  6. [6]

    Teleparallel Palatini theories

    J. Beltr´ an Jim´ enez, L. Heisenberg, and T. S. Koivisto, JCAP08, 039 (2018), arXiv:1803.10185 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  7. [7]

    Beltr´ an Jim´ enez, L

    J. Beltr´ an Jim´ enez, L. Heisenberg, T. S. Koivisto, and S. Pekar, Phys. Rev. D101, 103507 (2020), arXiv:1906.10027 [gr-qc]

    work page arXiv 2020

  8. [8]

    D. A. Gomes, J. Beltr´ an Jim´ enez, A. Jim´ enez Cano, and T. S. Koivisto, Phys. Rev. Lett.132, 141401 (2024), arXiv:2311.04201 [gr-qc]

    work page arXiv 2024

  9. [9]

    A. G. Bello-Morales, J. Beltr´ an Jim´ enez, A. Jim´ enez Cano, T. S. Koivisto, and A. L. Maroto, JHEP12, 146 (2024), arXiv:2406.19355 [gr-qc]

    work page arXiv 2024

  10. [10]

    Guzm´ an, L

    M.-J. Guzm´ an, L. J¨ arv, and L. Pati, Phys. Rev. D110, 124013 (2024), arXiv:2406.11621 [gr-qc]

    work page arXiv 2024

  11. [11]

    Beltr´ an Jim´ enez and T

    J. Beltr´ an Jim´ enez and T. S. Koivisto, Universe7, 143 (2021), arXiv:2104.05566 [gr-qc]

    work page arXiv 2021

  12. [12]

    D. G. Boulware and S. Deser, Phys. Rev. D6, 3368 (1972)

    1972

  13. [13]

    D. A. Gomes, J. Beltr´ an Jim´ enez, and T. S. Koivisto, JCAP12, 010 (2023), arXiv:2309.08554 [gr-qc]

    work page arXiv 2023

  14. [14]

    Hohmann, Int

    M. Hohmann, Int. J. Geom. Meth. Mod. Phys.18, 2140005 (2021), arXiv:2008.12186 [gr-qc]

    work page arXiv 2021

  15. [15]

    Ganz and M

    A. Ganz and M. Spinelli, (2025), arXiv:2511.19101 [gr- qc]

    work page arXiv 2025

  16. [16]

    J.-J. Chen, Z. Chen, and X. Gao, (2025), arXiv:2512.24298 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  17. [17]

    Beltr´ an Jim´ enez and T

    J. Beltr´ an Jim´ enez and T. S. Koivisto, Int. J. Geom. Meth. Mod. Phys.19, 2250108 (2022), arXiv:2202.01701 [gr-qc]

    work page arXiv 2022

  18. [18]

    Jensko, Class

    E. Jensko, Class. Quant. Grav.42, 055011 (2025), arXiv:2407.17568 [gr-qc]

    work page arXiv 2025

  19. [19]

    Resummation of Massive Gravity

    C. de Rham, G. Gabadadze, and A. J. Tolley, Phys. Rev. Lett.106, 231101 (2011), arXiv:1011.1232 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  20. [20]

    Deffayet, S

    C. Deffayet, S. Mukohyama, and A. Vikman, Phys. Rev. Lett.128, 041301 (2022), arXiv:2108.06294 [gr-qc]

    work page arXiv 2022

  21. [21]

    Global and local stability for ghosts coupled to positive energy degrees of freedom,

    C. Deffayet, A. Held, S. Mukohyama, and A. Vikman, JCAP11, 031 (2023), arXiv:2305.09631 [gr-qc]

    work page arXiv 2023

  22. [22]

    Deffayet, Aa

    C. Deffayet, A. Held, S. Mukohyama, and A. Vikman, Phys. Rev. D112, 065011 (2025), arXiv:2504.11437 [hep- th]

    work page arXiv 2025

  23. [23]

    Errasti D´ ıez, J

    V. Errasti D´ ıez, J. Gaset Rif` a, and G. Staudt, Fortsch. Phys.73, 2400268 (2025), arXiv:2408.16832 [hep-th]

    work page arXiv 2025

  24. [24]

    Errasti D´ ıez, J

    V. Errasti D´ ıez, J. G. Rif` a, and M. Lainz, Lect. Notes Comput. Sci.16035, 320 (2025), arXiv:2504.16169 [math-ph]

    work page arXiv 2025

  25. [25]

    A new formulation of Lee-Wick quantum field theory

    D. Anselmi and M. Piva, JHEP06, 066 (2017), arXiv:1703.04584 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  26. [26]

    On the quantum field theory of the gravitational interactions

    D. Anselmi, JHEP06, 086 (2017), arXiv:1704.07728 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  27. [27]

    Piva, Eur

    M. Piva, Eur. Phys. J. Plus138, 876 (2023), arXiv:2305.12549 [hep-th]

    work page arXiv 2023

  28. [28]

    J. M. Martin-Garcia, A. Garc´ ıa-Parrado, A. Stecchina, B. Wardell, C. Pitrou, D. Brizuela,et al.,http://www. xact.es(latest version Oct. 2021)

    2021