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Nonpropagating ghost in covariant $f(Q)$ gravity

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arxiv 2310.15507 v2 pith:ANYIEKMW submitted 2023-10-24 gr-qc astro-ph.COhep-th

Kun Hu , Makishi Yamakoshi , Taishi Katsuragawa , Shin'ichi Nojiri , Taotao Qiu This is my paper · ORCID
classification gr-qcastro-ph.COhep-th
keywords gravityscalarfieldsformulationmodecovariantghoststegr
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abstract

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity (STEGR). This work shows that based on the scalar-nonmetricity formulation, a scalar mode in $f(Q)$ gravity has a negative kinetic energy. This conclusion holds regardless of the coincident gauge frequently used in STEGR and $f(Q)$ gravity. To study the scalar mode, we further consider the covariant $f(Q)$ gravity as a special class in higher-order scalar tensor (HOST) theory and rewrite the four scalar fields, which play a role of the St\"{u}eckelberg fields associated with the diffeomorphism, by vector fields. Applying the standard Arnowitt-Deser-Misner (ADM) formulation to the new formulation of the $f(Q)$ gravity, we demonstrate that the ghost scalar mode can be eliminated by the second-class constraints, thus ensuring that $f(Q)$ gravity is a healthy theory.

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Cited by 4 Pith papers

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

  1. Degrees of freedom of a quadratic scalar-nonmetricity theory

    gr-qc 2025-12 conditional novelty 6.0 of 10

    In quadratic scalar-nonmetricity gravity, Hamiltonian analysis shows 10, 8, and 8 degrees of freedom for cases II, V, and VI, while linear cosmological perturbation theory sees only 10, 6, and 5, indicating hidden str...

  2. Revisiting Coincident GR in Internal STEGR Formulation

    gr-qc 2025-06 conditional novelty 5.0 of 10

    The paper derives internal-STEGR field equations, recovers coincident GR as the coincident-gauge sector, and finds that massive test particles obey a norm-flow equation instead of geodesics.

  3. ACT-DR6 consistent inflation in generalised entropic cosmology and $f(Q)$ gravity

    gr-qc 2026-07 conditional novelty 4.0 of 10

    Reconstruction produces explicit f(Q) and generalised-entropic inflation models (and scalar-coupled versions) whose slow-roll parameters match ACT-DR6 + Planck-BAO constraints on n_s and r.

  4. Properties of compact objects in quadratic non-metricity gravity

    gr-qc 2025-07 reject novelty 4.0 of 10

    Quadratic non-metricity gravity with a fitted coupling ξ can match PSR J0740+6620 while keeping the radial sound speed below c²/3, according to the paper's chosen metric ansatz.

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