Vacuum structure for scalar cosmological perturbations in Modified Gravity Models

TL;DR

This paper investigates the stability and causality of scalar cosmological perturbations in a broad class of Modified Gravity Models f(R,G), revealing potential instabilities and superluminal modes outside de Sitter backgrounds.

Contribution

It identifies a new vacuum instability and superluminal propagation conditions for scalar modes in general f(R,G) models, extending understanding beyond f(R) and f(G) theories.

Findings

Discovered a new instability in scalar modes outside de Sitter backgrounds.

Found that stable short-wavelength modes can be superluminal with group velocity depending on wave number.

Identified subclasses of models without these instabilities or superluminal features.

Abstract

We have found for the general class of Modified Gravity Models f(R,G) a new instability which can arise in vacuum for the scalar modes of the cosmological perturbations if the background is not de Sitter. In particular, the short-wavelength modes, if stable, in general have a group velocity which depends linearly in k, the wave number. Therefore these modes will be in general superluminal. We have also discussed the condition for which in general these scalar modes will be ghost-like. There is a subclass of these models, defined out of properties of the function f(R,G) and to which the f(R) and f(G) models belong, which however does not have this feature.