Arnowitt-Deser-Misner representation and Hamiltonian analysis of covariant renormalizable gravity

Abstract

We study the recently proposed Covariant Renormalizable Gravity (CRG), which aims to provide a generally covariant ultraviolet completion of general relativity. We obtain a space-time decomposed form --- an Arnowitt-Deser-Misner (ADM) representation --- of the CRG action. The action is found to contain time derivatives of the gravitational fields up to fourth order. Some ways to reduce the order of these time derivatives are considered. The resulting action is analyzed using the Hamiltonian formalism, which was originally adapted for constrained theories by Dirac. It is shown that the theory has a consistent set of constraints. It is, however, found that the theory exhibits four propagating physical degrees of freedom. This is one degree of freedom more than in Hořava-Lifshitz (HL) gravity and two more propagating modes than in general relativity. One extra physical degree of freedom has its origin in the higher order nature of the CRG action. The other extra propagating mode is a consequence of a projectability condition similarly as in HL gravity. Some additional gauge symmetry may need to be introduced in order to get rid of the extra gravitational degrees of freedom.

21 pages, LaTeX. A correction inserted to Hamiltonian formalism in Sec. 3

References in corpus (11)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Quantum Gravity at a Lifshitz Point
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Phenomenologically viable Lorentz-violating quantum gravity
• A dynamical inconsistency of Horava gravity
• Dark energy from modified gravity with Lagrange multipliers
• Modified F(R) Horava-Lifshitz gravity: a way to accelerating FRW cosmology
• Modified first-order Horava-Lifshitz gravity: Hamiltonian analysis of the general theory and accelerating FRW cosmology in power-law F(R) model
• A proposal for covariant renormalizable field theory of gravity
• Covariant power-counting renormalizable gravity: Lorentz symmetry breaking and accelerating early-time FRW universe
• Hamiltonian analysis of non-projectable modified F(R) Hořava-Lifshitz gravity

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