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

Abstract

We present analytic solutions to the Teukolsky equation for massless perturbations of any spin in the four-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 an analytic power series solution that 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.