Perturbation of FRW Spacetime in NP Formalism

TL;DR

This paper develops a unified and simplified formalism for analyzing perturbations in Friedmann-Robertson-Walker spacetime using Newman-Penrose formalism, providing analytic solutions for scalar, vector, and tensor modes.

Contribution

It introduces a master equation for all helicities in FRW spacetime and derives explicit solutions, including Green's functions and potentials, in a unified framework.

Findings

Unified master equation for all helicities in FRW perturbations

Analytic solutions for scalar, vector, and tensor modes

Explicit Green's functions and potentials derived

Abstract

Perturbation of FRW spacetime is carried out in NP formalism. The equation governing the scalar, vector and tensor modes take on a very simple and transparent form. All of them can be combined in one master equation for all helicities. The solutions for the closed, flat and open FRW are analytic continuation of the same functions, so only the solutions in the closed model are described. The scalar equation is the same as that of the conformally coupled massless Klein-Gordon field, the vectorial ones are the same as Maxwell equations, and the tensorial ones are for spin-2 fields. The corresponding eigen-functions are all determined, and in particular, the Green's function and the Lienard-Wiechert type potential also solved. These solutions reduce to the familiar form in flat space.