Lovelock-Brans-Dicke gravity

Abstract

According to Lovelock's theorem, the Hilbert-Einstein and the Lovelock actions are indistinguishable from their field equations. However, they have different scalar-tensor counterparts, which correspond to the Brans-Dicke and the \emph{Lovelock-Brans-Dicke} (LBD) gravities, respectively. In this paper the LBD model of alternative gravity with the Lagrangian density ${\mathcal{L}}_{\text{LBD}}=\frac{1}{16\pi }\left[\varphi \left(R+\frac{a}{\sqrt{-g}}{}^{\ast }RR+b\mathcal{G}\right)-\frac{{\omega }_{\text{L}}}{\varphi }{\nabla }_{\alpha }\varphi {\nabla }^{\alpha }\varphi \right]$ is developed, where ${}^{\ast }RR$ and $\mathcal{G}$ respectively denote the topological Chern-Pontryagin and Gauss-Bonnet invariants. The field equation, the kinematical and dynamical wave equations, and the constraint from energy-momentum conservation are all derived. It is shown that, the LBD gravity reduces to general relativity in the limit ${\omega }_{\text{L}}\to \infty$ unless the "topological balance condition" holds, and in vacuum it can be conformally transformed into the dynamical Chern-Simons gravity and the generalized Gauss-Bonnet dark energy with Horndeski-like or Galileon-like kinetics. Moreover, the LBD gravity allows for the late-time cosmic acceleration without dark energy. Finally, the LBD gravity is generalized into the Lovelock-scalar-tensor gravity, and its equivalence to fourth-order modified gravities is established. It is also emphasized that the standard expressions for the contributions of generalized Gauss-Bonnet dependence can be further simplified.

RevTex 13 pages. Minor changes are made to match the version published in Classical and Quantum Gravity

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Cited by in corpus (4)

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• Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants
• Scalar parity-odd trispectrum from gravitational Chern-Simons interaction vertices
• Chern-Simons gravitational term coupled to a spectator field