Quasinormal Ringing of de Sitter Braneworlds

TL;DR

This paper investigates the gravitational quasinormal modes of de Sitter braneworlds, revealing purely imaginary discrete modes that decay over time, influenced by brane structure and carrying cosmological constant information.

Contribution

It provides analytical and numerical analysis of gravitational perturbations in de Sitter branes, identifying the nature of quasinormal modes and their dependence on brane structure.

Findings

Quasinormal modes are purely imaginary and discrete.

The brane structure influences the quasinormal spectrum.

Modes decay without oscillation, carrying cosmological constant information.

Abstract

Compared with the Poincar\'e braneworld, the de Sitter (dS) braneworld aligns more closely with the present universe characterized by a small but finite cosmological constant. To explore the quasinormal ringing properties within the dS brane scenario, we investigate the gravitational perturbations in both thin and thick dS brane configurations. Analysis of the perturbation equations reveals that the effective potential along the extra dimension exhibits the shape of P\"oschl-Teller potential, asymptotically approaching a constant value (mass gap) at infinity. And analytical calculations further indicate that the gravitational perturbations, apart from the zero mode, possess a series of discrete, purely imaginary quasinormal modes in the late stages. This result implies that these perturbations decay without oscillation over time. The analytical findings also demonstrate that the brane structure primarily determines the distribution of the quasinormal spectrum while preserving the purely imaginary nature of the quasinormal frequencies. Subsequently, we further simulate the gravitational wave signal by numerically evolving the perturbation equations, which yield late-stage results consistent with the analytical predictions. Interestingly, these quasinormal modes carry information about the cosmological constant on the brane, which provides a potential new pathway for the study of cosmology in the dS brane scenario.