Relating metric and covariant perturbation theories in $f(R)$ gravity

TL;DR

This paper establishes a relationship between metric and covariant perturbation formalisms in $f(R)$ gravity, aiding researchers in translating results between these two approaches for cosmological inhomogeneities.

Contribution

It provides the first detailed comparison and translation framework between metric and covariant perturbation theories specifically for $f(R)$ gravity models.

Findings

Derived explicit relations between metric and covariant perturbations in $f(R)$ gravity.

Facilitated cross-formalism comparison for cosmological inhomogeneity studies.

Enhanced usability of perturbation results across different theoretical approaches.

Abstract

Modified theories of gravity have been invoked recently as an alternative to dark energy, in an attempt to explain the apparent accelerated expansion of the universe at the present time. In order to describe inhomogeneities in cosmological models, cosmological perturbation theory is used, of which two formalisms exist: the metric approach and the covariant approach. In this paper I present the relationship between the metric and covariant approaches for modeling $f(R)$ theories of gravity. This provides a useful resource that researchers primarily working with one formalism can use to compare or translate their results to the other formalism.