Nonlinear superhorizon perturbations in Horava-Lifshitz gravity

TL;DR

This paper develops a nonlinear analysis of superhorizon perturbations in Hořava-Lifshitz gravity, deriving solutions up to second order, demonstrating their extension to all orders, and establishing the conservation of a nonlinear curvature perturbation.

Contribution

It provides the first fully nonlinear gradient expansion solutions in Hořava-Lifshitz gravity and introduces a conserved nonlinear curvature perturbation analogous to the standard cosmological case.

Findings

Solutions are regular as λ approaches 1, recovering general relativity with dark matter.

The nonlinear curvature perturbation is conserved up to first order.

The method extends solutions to any order in the gradient expansion.

Abstract

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.