Stability of Singularity-free Cosmological Solutions in Ho\v{r}ava-Lifshitz Gravity

TL;DR

This paper investigates the stability of singularity-free bouncing cosmological solutions in Hořava-Lifshitz gravity, analyzing perturbations and their effects on the background, revealing conditions for stability and potential instabilities.

Contribution

It provides a detailed perturbation analysis of non-flat FLRW solutions in Hořava-Lifshitz gravity, identifying stability conditions and the impact of perturbations on bounce viability.

Findings

Scalar perturbation mass squared can be negative but stable due to Hubble friction.

Certain bouncing solutions are destabilized by perturbation backreaction.

Stable perturbations do not guarantee overall background stability in all cases.

Abstract

We study stability of singularity-free cosmological solutions with positive cosmological constant based on projectable Ho\v{r}ava-Lifshitz (HL) theory. In HL theory, the isotropic and homogeneous cosmological solutions with bounce can be realized if spacial curvature is non-zero. By performing perturbation analysis around non-flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime, we derive a quadratic action and discuss the stability, i.e, ghost and tachyon-free conditions. Although the squared effective mass of scalar perturbation must be negative in infrared regime, we can avoid tachyon instability by considering strong Hubble friction. Additionally, we estimate the backreaction from the perturbations on background geometry, especially, against anisotropic perturbation in closed FLRW spacetime. It turns out that certain types of bouncing solution may be spoiled even if all perturbation modes are stable.