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arXiv · 2310.15507

Nonpropagating ghost in covariant $f(Q)$ gravity

Kun Hu·Makishi Yamakoshi·Taishi Katsuragawa·Shin'ichi Nojiri·Taotao Qiu
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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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Kun Hu, Makishi Yamakoshi, Taishi Katsuragawa, Shin'ichi Nojiri, Taotao Qiu. 2023-10-24. Nonpropagating ghost in covariant $f(Q)$ gravity. https://arxiv.org/abs/2310.15507

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