Constraining $f(R)$ gravity by the Large Scale Structure

TL;DR

This paper reviews how certain $f(R)$ gravity models can be constrained using large-scale structure data, addressing modifications to General Relativity and dark sector puzzles.

Contribution

It provides a comprehensive review of $f(R)$ gravity models compatible with cosmological and local constraints, emphasizing their testability with large-scale structure.

Findings

Some $f(R)$ models are consistent with both cosmological and local gravity constraints.

Large Scale Structure can effectively constrain classes of $f(R)$ gravity models.

The review highlights the potential of galaxy clusters and N-Body simulations in testing modified gravity.

Abstract

Over the past decades, General Relativity and the concordance $\Lambda$CDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets ({\it precision cosmology}). Despite their successes, some shortcomings emerge due to the fact that General Relativity should be revised at infrared and ultraviolet limits and to the fact that the fundamental nature of Dark Matter and Dark Energy is still a puzzle to be solved. In this perspective, $f(R)$ gravity have been extensively investigated being the most straightforward way to modify General Relativity and to overcame some of the above shortcomings. In this paper, we review various aspects of $f(R)$ gravity at extragalactic and cosmological levels. In particular, we consider cluster of galaxies, cosmological perturbations, and N-Body simulations, focusing on those models that satisfy both cosmological and local gravity constraints. The perspective is that some classes of $f(R)$ models can be consistently constrained by Large Scale Structure.