Hamiltonian analysis of linearized extension of Ho?ava-Lifshitz gravity

摘要

We investigate the Hamiltonian structure of linearized extended Ho?ava-Lifshitz gravity in a flat cosmological background following the Faddeev-Jackiw's Hamiltonian reduction formalism. The Hamiltonian structure of extended Ho?ava-Lifshitz gravity is similar to that of the projectable version of original Ho?ava-Lifshitz gravity, in which there is one primary constraint and so there are two physical degrees of freedom. In the infrared (IR) limit, however, there is one propagating degree of freedom in the general cosmological background, and that is coupled to the scalar graviton mode. We find that extra scalar graviton mode in an inflationary background can be decoupled from the matter field in the IR limit. But it is necessary to go beyond linear order in order to draw any conclusion of the strong coupling problem.