Notes on diffeomorphisms symmetry of $f(R)$ gravity in the cosmological context

TL;DR

This paper investigates how restricted $f(R)$ gravity affects metric perturbations in cosmology, showing that certain parameters can eliminate anisotropic stress and identifying constraints to ensure stability of perturbations.

Contribution

It introduces a parameter to restrict diffeomorphisms in $f(R)$ gravity, enabling removal of anisotropic stress and establishing stability conditions for perturbations.

Findings

Parameter choice removes anisotropic stress.

Constraints prevent instability in vector and tensor modes.

Provides a framework for stable restricted $f(R)$ cosmology.

Abstract

We study the metric perturbations in the context of restricted $f(R)$ gravity, in which a parameter for deviation from the full diffeomorphisms of space-time is introduced. We demonstrate that one can choose the parameter to remove the induced anisotropic stress, which is present in the usual $f(R)$ gravity. Moreover, to prevent instability for the vector and tensor metric perturbations, some constraints on the model are obtained.