Inevitable ghost and the degrees of freedom in f(R,G) gravity

TL;DR

This paper investigates linear perturbations in f(R,G) gravity on anisotropic Kasner backgrounds, revealing that ghost degrees of freedom are present unless the background is isotropic, where one mode decouples.

Contribution

It demonstrates that anisotropic backgrounds in f(R,G) gravity generally contain ghost degrees of freedom, unlike FLRW backgrounds where ghosts are absent.

Findings

Anisotropic Kasner background has four propagating degrees of freedom.

On FLRW backgrounds, the degrees of freedom reduce to three.

Presence of a ghost mode when the extra mode remains physical.

Abstract

The study of linear perturbation theory for general functions of the Ricci and Gauss-Bonnet scalars is done over an empty anisotropic universe, i.e. the Kasner-type background, in order to show that an anisotropic background in general has ghost degrees of freedom, which are absent on Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds. The study of the scalar perturbation reveals that on this background the number of independent propagating degrees of freedom is four and reduces to three on FLRW backgrounds, as one mode becomes highly massive to decouple from the physical spectrum. When this mode remains physical, there is inevitably a ghost mode.