Analytic solutions of the Teukolsky equation for massless perturbations of any spin in de Sitter background

TL;DR

This paper derives exact analytic solutions to the Teukolsky equation for massless fields of any spin in de Sitter space, providing insights into wave behavior and spectral properties in this cosmological background.

Contribution

It presents the first complete analytic solutions for the Teukolsky equation in de Sitter space, including hypergeometric polynomial solutions and spectral analysis.

Findings

Discrete and continuous wave frequency spectra identified

Explicit polynomial solutions with specific spectral properties derived

Regular power series solutions at the poles obtained

Abstract

We present analytic solutions to the Teukolsky equation for massless perturbations of any spin in the 4-dimensional de Sitter background. The angular part of the equation fixes the separation constant to a discrete set and its solution is given by hypergeometric polynomials. For the radial part, we derive analytic power series solution which is regular at the poles and determine a transcendental function whose zeros give the characteristic values of the wave frequency. We study the existence of explicit polynomial solutions to the radial equation and obtain two classes of singular closed-form solutions, one with discrete wave frequencies and the other with continuous frequency spectra.