Nonpropagating ghost in covariant gravity
arXiv:2310.15507
Abstract
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 gravity has a negative kinetic energy. This conclusion holds regardless of the coincident gauge frequently used in STEGR and gravity. To study the scalar mode, we further consider the covariant gravity as a special class in higher-order scalar tensor (HOST) theory and rewrite the four scalar fields, which play a role of the Stüeckelberg fields associated with the diffeomorphism, by vector fields. Applying the standard Arnowitt-Deser-Misner (ADM) formulation to the new formulation of the gravity, we demonstrate that the ghost scalar mode can be eliminated by the second-class constraints, thus ensuring that gravity is a healthy theory.
31 pages, 0 figures