Cosmological perturbations in Horava-Lifshitz theory without detailed balance

TL;DR

This paper analyzes linear scalar perturbations in a generalized Horava-Lifshitz gravity theory without detailed balance, revealing stability and ghost issues of the scalar graviton mode across different scales.

Contribution

It computes the scalar perturbations in the most general Horava-Lifshitz theory without detailed balance, highlighting stability and ghost problems of the scalar mode.

Findings

Higher-order curvature terms induce effective anisotropic stress.

Scalar mode is stable for 0 ≤ ξ ≤ 2/3.

Scalar mode is a ghost within the stability range.

Abstract

In the Horava-Lifshitz theory of quantum gravity, two conditions -- detailed balance and projectability -- are usually assumed. The breaking of projectability simplifies the theory, but it leads to serious problems with the theory. The breaking of detailed balance leads to a more complicated form of the theory, but it appears to resolve some of the problems. Sotiriou, Visser and Weinfurtner formulated the most general theory of Horava-Lifshitz type without detailed balance. We compute the linear scalar perturbations of the FRW model in this form of HL theory. We show that the higher-order curvature terms in the action lead to a gravitational effective anisotropic stress on small scales. Specializing to a Minkowski background, we study the spin-0 scalar mode of the graviton, using a gauge-invariant analysis, and find that it is stable in both the infrared and ultraviolet regimes for $0 \le \xi \le 2/3$. However, in this parameter range the scalar mode is a ghost.