The Equation of State Approach to Cosmological Perturbations in f(R) Gravity

TL;DR

This paper develops an equation of state formalism for linear cosmological perturbations in f(R) gravity, enabling a fluid-like description of modifications to General Relativity across scalar, vector, and tensor modes.

Contribution

It provides explicit expressions for perturbation variables in f(R) gravity using the EoS approach, facilitating a unified treatment of modifications as a dark-energy-fluid.

Findings

Explicit EoS expressions for scalar, vector, tensor perturbations

Perturbed variables expressed in terms of model parameters

Framework applicable to various f(R) models

Abstract

The discovery of apparent cosmological acceleration has spawned a huge number of dark energy and modified gravity theories. The f(R) models of gravity are obtained when one replaces the Ricci scalar in the Einstein-Hilbert action by an arbitrary function of the Ricci scalar. In this work we provide expressions for the equations of state (EoS) for perturbations which completely characterize the linearized perturbations in f(R) gravity, including the scalar, vector, and tensor modes. The EoS formalism is a powerful and elegant parametrization where the modification to General Relativity are treated as a dark-energy-fluid. The perturbed dark-energy-fluid variables such as the anisotropic stress or the entropy perturbation are explicitly given in terms of parameters of the model of interest.