Dynamical Scalar Degree of Freedom in Horava-Lifshitz Gravity

Understand

We investigate the linear cosmological perturbations of Ho\v{r}ava-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 $\lambda=1$, the dynamical scalar degree of freedom turns to be a non-dynamical one at the linear order level.