# Cosmological perturbations in the Regge-Wheeler formalism

## TL;DR

This paper adapts the Regge-Wheeler formalism, traditionally used for black hole perturbations, to analyze linear cosmological perturbations in FLRW models, revealing a structured approach to gravitational and matter fluctuations.

## Contribution

It demonstrates that linear cosmological perturbations can be expressed through master scalars satisfying wave equations, extending the Regge-Wheeler formalism to cosmology.

## Key findings

- Perturbations are represented by two master scalars obeying wave equations.
- Matter perturbations are described by a scalar satisfying a transport equation.
- The formalism can potentially be extended to nonlinear perturbations.

## Abstract

We study linear perturbations of the Friedmann-Lemaitre-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 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 (conformal) matter perturbation. We expect the Regge-Wheeler formalism to be easily extended to include nonlinear perturbations, akin to to the recent work [Phys. Rev. D 96, 124026 (2017)].