Models for the Brane-Bulk Interaction: Toward Understanding Braneworld Cosmological Perturbation

TL;DR

This paper investigates brane-bulk interactions in cosmological models with extra dimensions using toy models to understand dissipation and nonlocal effects caused by bulk gravitons, relevant for braneworld cosmology.

Contribution

It introduces simplified models to analyze the dynamics of brane-bulk interactions, capturing key features of cosmological perturbations in braneworld scenarios.

Findings

Bulk gravitons induce dissipation and nonlocality on the brane.

Models replicate qualitative features of linearized cosmological perturbations.

Analysis includes systems with and without time translation invariance.

Abstract

Using some simple toy models, we explore the nature of the brane-bulk interaction for cosmological models with a large extra dimension. We are in particular interested in understanding the role of the bulk gravitons, which from the point of view of an observer on the brane will appear to generate dissipation and nonlocality, effects which cannot be incorporated into an effective (3+1)-dimensional Lagrangian field theoretic description. We explicitly work out the dynamics of several discrete systems consisting of a finite number of degrees of freedom on the boundary coupled to a (1+1)-dimensional field theory subject to a variety of wave equations. Systems both with and without time translation invariance are considered and moving boundaries are discussed as well. The models considered contain all the qualitative feature of quantized linearized cosmological perturbations for a Randall-Sundrum universe having an arbitrary expansion history, with the sole exception of gravitational gauge invariance, which will be treated in a later paper.