Linearization of a warped f (R) theory in the higher-order frame. II. the equation of motion approach

Without using conformal transformation, a simple type of five-dimensional f(R)-brane model is linearized directly in its higher-order frame. In this paper, the linearization is conducted in the equation of motion approach. We first derive all the linear perturbation equations without specifying a gauge condition. Then, by taking the curvature gauge, we derive the master equations of the linear perturbations. We show that these equations are equivalent to those obtained in the quadratical action approach [Phys. Rev. D 95, 104060 (2017)PRVDAQ2470-001010.1103/PhysRevD.95.104060], except the vector sector, in which a constraint equation can be obtained in the equation of motion approach but is absent in the quadratical action approach. Our work sets an example on how to linearize higher-order theories without using conformal transformation, and might be useful for studying more complicated theories.