Coupled bulk and brane fields about a de Sitter brane

TL;DR

This paper analyzes the spectral properties of coupled bulk and brane scalar fields in a de Sitter brane setup, revealing conditions for bound states, resonances, and tachyonic instabilities, with both analytical and numerical insights.

Contribution

It provides a detailed spectral analysis of coupled bulk-brane scalar fields in a de Sitter brane context, including the development of a numerical code for evolving such systems.

Findings

Existence of zero, one, or two bound states depending on parameters.

Identification of a critical coupling leading to tachyonic bound states.

Good agreement between analytical spectral analysis and numerical simulations.

Abstract

We consider the evolution of a bulk scalar field in anti-de Sitter (AdS) spacetime linearly coupled to a scalar field on a de Sitter boundary brane. We present results of a spectral analysis of the system, and find that the model can exhibit both bound and continuum resonant modes. We find that zero, one, or two bound states may exist, depending upon the masses of the brane and bulk fields relative to the Hubble length and the AdS curvature scale and the coupling strength. In all cases, we find a critical coupling above which there exists a tachyonic bound state. We show how the 5-dimensional spectral results can be interpreted in terms of a 4-dimensional effective theory for the bound states. We find excellent agreement between our analytic results and the results of a new numerical code developed to model the evolution of bulk fields coupled to degrees of freedom on a moving brane. This code can be used to model the behaviour of braneworld cosmological perturbations in scenarios for which no analytic results are known.