[Paper Review] Linear perturbations of cosmological models in the Horava-Lifshitz theory of gravity without detailed balance

Anzhong Wang, Roy Maartens|arXiv (Cornell University)|Jul 10, 2009

Cosmology and Gravitation Theories21 citations

TL;DR

This paper investigates linear scalar perturbations in Friedmann-Robertson-Walker (FRW) cosmological models within the Horava-Lifshitz gravity framework without detailed balance, using a gauge-invariant approach. It finds that the spin-0 scalar mode of the graviton remains stable in both infrared and ultraviolet regimes for $0 \leq \xi \leq 2/3$, but is a ghost in this range, indicating a fundamental instability despite dynamical stability.

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.

Motivation & Objective

• To analyze linear scalar perturbations in FRW models within Horava-Lifshitz gravity without the detailed balance condition.
• To assess the stability and physical viability of the spin-0 scalar mode of the graviton in the absence of detailed balance.
• To determine the parameter range where the scalar mode remains stable across both infrared and ultraviolet regimes.
• To evaluate whether the absence of detailed balance resolves issues arising from projectable versions of the theory.

Proposed method

• Utilizes the most general form of Horava-Lifshitz gravity without detailed balance, as formulated by Sotiriou, Visser, and Weinfurtner.
• Applies a gauge-invariant formalism to study scalar perturbations in a spatially flat FRW background.
• Analyzes the effective gravitational anisotropic stress induced by higher-order curvature terms in the action at small scales.
• Performs a linearized analysis of the spin-0 scalar mode on a Minkowski background to assess stability.
• Employs a parameter $\xi$ to characterize the theory's behavior, focusing on the range $0 \leq \xi \leq 2/3$.
• Evaluates the nature of the scalar mode (ghost or healthy) by examining its kinetic term and energy sign.

Experimental results

Research questions

• RQ1 How do linear scalar perturbations behave in FRW models within Horava-Lifshitz gravity without detailed balance?
• RQ2 Is the spin-0 scalar mode of the graviton stable across both infrared and ultraviolet regimes in the absence of detailed balance?
• RQ3 For which values of the parameter $\xi$ is the scalar mode stable, and what is its physical nature in that range?
• RQ4 Does removing detailed balance resolve the ghost-like behavior seen in earlier formulations of the theory?
• RQ5 What is the role of higher-order curvature terms in generating effective anisotropic stress on small scales?

Key findings

• The spin-0 scalar mode of the graviton is stable in both the infrared and ultraviolet regimes for the parameter range $0 \leq \xi \leq 2/3$.
• Despite this dynamical stability, the scalar mode is a ghost in the same range, indicating a negative kinetic energy and potential instability.
• Higher-order curvature terms in the action generate an effective anisotropic stress on small scales, modifying the gravitational dynamics.
• The absence of detailed balance leads to a more complex action but avoids certain pathologies present in the detailed balance formulation.
• The gauge-invariant analysis confirms that the scalar mode's behavior is consistent across different scales and does not exhibit secular growth.
• The parameter $\xi$ plays a critical role in determining the stability and ghost nature of the scalar mode, with $\xi = 0$ and $\xi = 2/3$ marking the boundaries of the stable but ghostly regime.