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

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.

15 pages

References in corpus (4)

• f(R)-Brane
• Theory of gravitation theories: a no-progress report
• Domain wall brane in squared curvature gravity
• Tensor perturbations of $f(R)$-branes

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• Characteristic modes of thick brane model: resonances and quasinormal modes
• Tensor Perturbations and Thick Branes in Higher-dimensional $f(R)$ Gravity
• Linearization of a warped $f(R)$ theory in the higher-order frame II: the equation of motion approach
• Quasinormal ringing of thick braneworlds with a finite extra dimension
• Graviscalar quasinormal modes and asymptotic tails of a thick brane
• Linear Perturbations and Stability Analysis in $f(T)$ Braneworld Scenario