Hamiltonian analysis of Linearized Extension of Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper analyzes the Hamiltonian structure of linearized extended Hořava-Lifshitz gravity in a flat cosmological background, revealing similarities to the original theory and discussing the decoupling of scalar modes in different backgrounds.

Contribution

It provides a Hamiltonian analysis of the extended Hořava-Lifshitz gravity, highlighting the degrees of freedom and mode coupling in various cosmological backgrounds.

Findings

Hamiltonian structure similar to projectable Hořava-Lifshitz gravity

Extra scalar graviton decouples in IR limit during inflation

Coupling between scalar mode and matter depends on background

Abstract

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