Dynamical Scalar Degree of Freedom in Horava-Lifshitz Gravity

Abstract

We investigate the linear cosmological perturbations of Hořava-Lifshitz gravity in a FRW universe without any matter. Our results show that a new gauge invariant dynamical scalar mode emerges, due to the gauge transformation under the "foliation-preserving" diffeomorphism and "projectability condition", and it can produce a scale invariant power spectrum. In the infrared regime with $λ=1$, the dynamical scalar degree of freedom turns to be a non-dynamical one at the linear order level.

5pages, no figures, references added, version to appear in PRD(R)