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arXiv · 2202.11881

Modified-gravity theories with nondynamical background fields

Carlos M. Reyes·Marco Schreck
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Abstract

We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{μν}$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work. The computations show that the dynamical field equations obtained from the Lagrangian and Hamiltonian approaches are consistent with each other. Connections to Brans-Dicke theory and ghost-free massive gravity are established.

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Carlos M. Reyes, Marco Schreck. 2022-02-24. Modified-gravity theories with nondynamical background fields. https://doi.org/10.1103/physrevd.106.044050

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