f(R) as a dark energy fluid

TL;DR

This paper demonstrates that f(R) modified gravity models can be reformulated as a dark energy fluid, simplifying the analysis of cosmological perturbations by expressing their evolution through equations of state.

Contribution

It introduces a novel approach to describe f(R) gravity perturbations as a dark energy fluid, eliminating the scalar degree of freedom for easier analysis.

Findings

Perturbations can be characterized by equations of state for entropy and anisotropic stress.

The reformulation simplifies the evolution equations for scalar, vector, and tensor sectors.

Numerical evolution of perturbations confirms the simplicity of the fluid description.

Abstract

We study the equations for the evolution of cosmological perturbations in $f\left(\mathcal{R}\right)$ and conclude that this modified gravity model can be expressed as a dark energy fluid at background and linearised perturbation order. By eliminating the extra scalar degree of freedom known to be present in such theories, we are able to characterise the evolution of the perturbations in the scalar sector in terms of equations of state for the entropy perturbation and anisotropic stress which are written in terms of the density and velocity perturbations of the dark energy fluid and those in the matter, or the metric perturbations. We also do the same in the much simpler vector and tensor sectors. In order to illustrate the simplicity of this formulation, we numerically evolve perturbations in a small number of cases.