  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.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics