A model independent approach to the study of structure growth in $f(R)$ gravity

TL;DR

This paper introduces a model-independent method to analyze the background and growth of matter perturbations in f(R) gravity models that replicate ΛCDM expansion, using cosmography and dimensionless variables.

Contribution

It develops a novel, model-independent framework for studying f(R) gravity's background and perturbation growth without specifying the f(R) function.

Findings

The method accurately reproduces ΛCDM-like background evolution.

Comparison shows the quasi-static approximation closely matches exact growth for certain models.

The approach validates using cosmography to test modified gravity theories.

Abstract

Over the last decade, much attention has been given to the study of modified gravity theories to find a more natural explanation for the late-time acceleration of the Universe. Particular attention has focused on the so-called $f(R)$ dark energy models. Instead of focusing on a particular f(R) model, we present a completely model-independent approach to study the background dynamics and the growth of matter density perturbations for those f(R) models that mimic the $\Lambda$CDM evolution at the background level. We do this by characterising the dynamics of the gravitational field using a set of dimensionless variables and using cosmography to determine the expansion history. We then illustrate the integrity of this method by fixing the cosmography to be the same as an exact $\Lambda$CDM model, allowing us to test the solution. We compare the exact evolution of the density contrast and growth index with what one obtains from various levels of the quasi-static approximation, without choosing the form of $f(R)$ dark energy.