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

  • Masud Chaichian
  • Markku Oksanen
  • Anca TureanuEmail author
Regular Article - Theoretical Physics

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 spacetime 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.

Keywords

Poisson Bracket Canonical Variable Shift Vector Hamiltonian Constraint Physical Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2011

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of HelsinkiHelsinkiFinland

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