de Sitter spacetime: effects of metric perturbations on geodesic motion

TL;DR

This paper investigates how metric perturbations affect geodesic motion in de Sitter spacetime, deriving equations using the Regge--Wheeler formalism and analyzing spectral properties and gauge-invariant perturbations.

Contribution

It introduces a reduction of perturbation equations to a Heun-type differential equation and explores solutions relevant to geodesic deviations and spectral analysis in de Sitter space.

Findings

Derived a single second order differential equation for perturbations.

Analyzed deviation of geodesics due to perturbations.

Discussed existence of closed-form solutions to the Teukolsky equation.

Abstract

Gravitational perturbations of the de Sitter spacetime are investigated using the Regge--Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gauge- and tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.