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 Lovelock-Brans-Dicke (LBD) gravities, respectively. In this paper the LBD model of alternative gravity with the Lagrangian densitywhere * RR and 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 ω L → ∞ 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.

de Sitter and power-law solutions in some models of modified gravity

“…As explained in the Introduction, non-local gravity can be generalized further to non-local Brans-Dicke (BD) gravity. 9 The corresponding action of the system is…”

“…It has been shown by different authors that these non-local terms ccould be responsible for both inflation and the current cosmic acceleration (see, e.g., [23][24][25] ). On the other hand, a convincing motivation for the extension of Brans-Dicke (BD) gravity has been recently given in, 9 namely that alternative and modified gravities actually encode possible ways to go beyond Lovelock's theorem and its necessary conditions, which limit the second-order field equation in four dimensions to essentially Einstein's equation supplemented by the cosmological constant. In this way, similarly to what happened with the introduction of extended GR theories, extensions of BD gravity naturally come into play.…”

Properties of Spherically Symmetric Black Holes in the Generalized Brans–Dicke Modified Gravitational Theory

“…We consider a specific parametric model [54,55]: φ(r) = φ 0 r −a and f (R) = R + βR (−n) . Under the background of the spherically symmetric space-time line elements:…”

n + 1 formalism of f (Lovelock) gravity

“…Even for n + 1 = 4, although the Gauss-Bonnet term is the integrand of a topological invariant, this is not the case anymore when it is coupled to a scalar field. The application of a scalar−tensor approach à la Brans-Dicke to Gauss-Bonnet theories gives physically different results (see [21], or [22] for a model that lets the torsion be different from zero).…”