Anisotropic stress and stability in modified gravity models

TL;DR

This paper investigates higher order gravity models of the f(R,G) type, identifying conditions for zero anisotropic stress and exploring implications for model stability and viability, especially in de Sitter backgrounds.

Contribution

It finds a subclass of f(R,G) models with zero anisotropic stress and links anisotropic stress to stability and extra degrees of freedom in these models.

Findings

A subclass of models with zero anisotropic stress in de Sitter space.

Zero anisotropic stress leads to singularities preventing de Sitter evolution.

Anisotropic stress is connected to model stability and extra degrees of freedom.

Abstract

The existence of anisotropic stress of a purely geometrical origin seems to be a characteristic of higher order gravity models, and has been suggested as a probe to test these models observationally, for example in weak lensing experiments. In this paper, we seek to find a class of higher order gravity models of f(R,G) type that would give us a zero anisotropic stress and study the consequences for the viability of the actual model. For the special case of a de Sitter background, we identify a subclass of models with the desired property. We also find a direct link between anisotropic stress and the stability of the model as well as the presence of extra degrees of freedom, which seems to be a general feature of higher order gravity models. Particularly, setting the anisotropic stress equal to zero for a de Sitter background leads to a singularity that makes it impossible to reach the de Sitter evolution.