Scalar field perturbations in Horava-Lifshitz cosmology

TL;DR

This paper analyzes scalar field perturbations within Horava-Lifshitz gravity, deriving a sixth-order Klein-Gordon equation and examining their behavior during inflation, revealing independent oscillations on sub-horizon scales and conserved curvature perturbations on super-horizon scales.

Contribution

It provides the first detailed derivation of scalar perturbations in Horava-Lifshitz cosmology without detailed balance, including the generalized sixth-order Klein-Gordon equation and their evolution during inflation.

Findings

Scalar perturbations have independent oscillations on sub-horizon scales.

Curvature perturbation remains constant on super-horizon scales during inflation.

The generalized Klein-Gordon equation is sixth-order in spatial derivatives.

Abstract

We study perturbations of a scalar field cosmology in Horava-Lifshitz gravity, adopting the most general setup without detailed balance but with the projectability condition. We derive the generalized Klein-Gordon equation, which is sixth-order in spatial derivatives. Then we investigate scalar field perturbations coupled to gravity in a flat Friedmann-Robertson-Walker background. In the sub-horizon regime, the metric and scalar field modes have independent oscillations with different frequencies and phases except in particular cases. On super-horizon scales, the perturbations become adiabatic during slow-roll inflation driven by a single field, and the comoving curvature perturbation is constant.