Nonlinear superhorizon perturbations in Horava-Lifshitz gravity

Understand

We perform a fully nonlinear analysis of superhorizon perturbation in Ho\v{r}ava-Lifshitz gravity, based on the gradient expansion method.

• We present a concrete expression for the solution of gravity equations up to the second order in the gradient expansion, and prove that the solution can be extended to any order.
• The result provides yet another example for analogue of the Vainshtein effect: the nonlinear solution is regular in the limit $\lambda\to 1$ and recovers general relativity coupled to dark matter at low energy.
• Finally, we propose a definition of nonlinear curvature perturbation ${\cal R}$ in Ho\v{r}ava-Lifshitz gravity and show that it is conserved up to the first order in the gradient expansion.