Cosmological perturbations in the Regge-Wheeler formalism

We study linear perturbations of the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model in the Regge-Wheeler formalism, which is a standard framework to study perturbations of spherically symmetric black holes. In particular, we show that the general solution of linear perturbation equations can be given in terms of two copies of a master scalar satisfying the scalar wave equation on the FLRW background (with a Regge-Wheeler/Zerilli type potential), thus representing two gravitational degrees of freedom and one scalar satisfying a transport type equation representing matter perturbation. We expect the Regge-Wheeler formalism to be easily extended to include nonlinear perturbations, akin to the recent work [A. Rostworowski, Phys. Rev. D 96, 124026 (2017), 10.1103/PhysRevD.96.124026].