Nonlinear superhorizon perturbations in Horava-Lifshitz gravity

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.