Hamiltonian analysis of spatially covariant gravity
Abstract
We perform the Hamiltonian constraint analysis for a wide class of gravity theories that are invariant under spatial diffeomorphism. With a very general setup, we show that different from the general relativity, the primary and secondary constraints associated with the lapse function N become second class, as long as the lapse function N enters the Hamiltonian nonlinearly. This fact implies that there are 3 degrees of freedom are propagating, of which two correspond to the usual tensor-type transverse and traceless gravitons, and one is the scalar-type graviton. By restoring the full spacetime diffeomorphism using the Stückelberg trick, this type of spatially covariant gravity theory corresponds to a large class of single field scalar-tensor theories that possess higher order derivatives in the equations of motion, and thus is beyond the scope of the Horndeski theory.
- Publication:
-
Physical Review D
- Pub Date:
- November 2014
- DOI:
- 10.1103/PhysRevD.90.104033
- arXiv:
- arXiv:1409.6708
- Bibcode:
- 2014PhRvD..90j4033G
- Keywords:
-
- 04.50.Kd;
- Modified theories of gravity;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- v1: 17 pages