Linearization of a warped $f(R)$ theory in the higher-order frame

TL;DR

This paper investigates the linearization of a specific $f(R)$ gravity model in a higher-order frame within a five-dimensional warped spacetime, deriving quadratic actions for perturbations and comparing them to Einstein frame results.

Contribution

It provides a detailed derivation of quadratic actions for scalar, vector, and tensor perturbations in the higher-order frame of $f(R)$ gravity, demonstrating their equivalence to Einstein frame results.

Findings

Quadratic actions for perturbations are derived in the higher-order frame.

Perturbation equations reduce to second order under the curvature gauge.

Quadratic actions are equivalent in the higher-order and Einstein frames.

Abstract

The linearization of a type of $f(R)$ gravity is studied directly in the higher-order frame for an arbitrary five-dimensional warped space-time background. The quadratic actions of the normal modes of the scalar, vector, and tensor perturbations are derived by taking the curvature gauge, under which the linear perturbation of the scalar curvature is zero, and all the perturbation equations reduce to second order. By comparing our results to those obtained in the Einstein frame, we find that the quadratic actions of the normal modes are equivalent for these two frames.