Quasinormal modes and dual resonant states on de Sitter space

TL;DR

This paper rigorously establishes the existence of quasinormal modes for scalar fields in de Sitter space across all dimensions and masses, introducing a method to explicitly compute these modes and highlighting the role of dual resonant states.

Contribution

It provides a definitive proof of quasinormal modes existence in de Sitter space and introduces a simple calculation method, emphasizing the importance of dual resonant states.

Findings

Confirmed existence of QNMs for all scalar field masses and dimensions

Developed a straightforward method for calculating QNMs and mode solutions

Highlighted the role of dual resonant states in QNM expansions

Abstract

The existence of quasinormal modes (QNMs) for waves propagating on pure de Sitter space has been called into question in several works. We definitively prove the existence of quasinormal modes for massless and massive scalar fields in all dimensions and for all scalar field masses, and present a simple method for the explicit calculation of QNMs and the corresponding mode solutions. By passing to coordinates which are regular at the cosmological horizon, we demonstrate that certain QNMs only appear in the QNM expansion of the field when the initial data do not vanish near the cosmological horizon. The key objects in the argument are dual resonant states. These are distributional mode solutions of the adjoint field equation satisfying a generalized incoming condition at the horizon, and they characterize the amplitudes with which QNMs contribute to the QNM expansion of the field.