Covariant gauge invariant theory of Scalar Perturbations in $f(R)$-gravity: a brief review

TL;DR

This paper reviews the covariant gauge invariant approach to scalar perturbations in $f(R)$-gravity, analyzing structure formation, characteristic signatures, and implications of these models.

Contribution

It provides a comprehensive review of the current state of covariant gauge invariant perturbation theory in $f(R)$-gravity, highlighting key signatures and their physical implications.

Findings

Characteristic signatures identified in $f(R)$-gravity models

Implications for structure formation in modified gravity

Critical analysis of perturbation results

Abstract

I review the state of the art of the investigation on the structure formation in $f(R)$-gravity based on the Covariant and Gauge Invariant approach to perturbations. A critical analysis of the results, in particular the presence of characteristic signature of these models, together with their meaning and their implication is given.