Modified-gravity theories with nondynamical background fields

TL;DR

This paper investigates a modified gravity theory with nondynamical background fields, analyzing its dynamics through ADM decomposition and Hamiltonian formalism, and establishing connections to Brans-Dicke and massive gravity theories.

Contribution

It introduces a modified gravity framework with nondynamical backgrounds, deriving consistent field equations via Lagrangian and Hamiltonian methods, and links to other gravity models.

Findings

Consistent dynamical equations from Lagrangian and Hamiltonian approaches.

Extended Gibbons-Hawking-York boundary term incorporated.

Connections to Brans-Dicke and ghost-free massive gravity established.

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 $s^{\mu\nu}$ 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.