Quasinormal modes in pure de sitter spacetimes

TL;DR

We address the quasinormal mode spectrum of scalar and fermion perturbations in pure and topological de Sitter spacetimes. The analysis combines mode separation, a Schrödinger-like radial equation with a solvable potential, and hypergeometric functions to impose the horizon-outgoing and origin-vanishing boundary conditions; for scalars, a mass threshold $m > \frac{d-1}{2l}$ is required for well-defined QNMs, with frequencies $\omega = -\frac{i}{l}(2n+\ell+h_\pm)$ or $-\frac{i}{l}(2n-\ell-d+3+h_\pm)$, $h_\pm = \frac{d-1}{2}-\sqrt{(\frac{d-1}{2})^2-m^2l^2}$. In topological dS spaces the potential leads to growing modes and instability, while 3D fermions exhibit QNMs for non-s-wave modes but not for $\ell=0$; 4D fermions yield analogous spectra with $\kappa_\pm$-dependent branches and $\omega$ containing $\pm m$ in the real part. These results illuminate the stability and spectral structure of perturbations in de Sitter spacetimes and bear on discussions of dS/CFT and horizon thermodynamics.

Abstract

We have studied scalar perturbations as well as fermion perturbations in pure de Sitter space-times. For scalar perturbations we have showed that well-defined quasinormal modes can exist provided that the mass of scalar field $m>\frac{d-1}{2l}$. The quasinormal frequencies of fermion perturbations in three and four dimensional cases have also been presented. We found that different from other dimensional cases, in three dimensional pure de Sitter spacetime there is no quasinormal mode for the s-wave. This interesting difference caused by the spacial dimensions is true for both scalar and fermion perturbations.