Braneworld Dynamics of Inflationary Cosmologies with Exponential Potentials

TL;DR

This paper analyzes the dynamics of inflationary cosmologies within Randall-Sundrum braneworld models using dynamical systems, focusing on scalar fields with exponential potentials and how their behavior differs from general relativity.

Contribution

It provides a systematic dynamical systems analysis of braneworld inflationary models with exponential potentials, highlighting new critical points and bifurcations compared to general relativity.

Findings

Identification of new critical points in braneworld models

Changes in the structure of state spaces due to extra dimensions

Occurrence of bifurcations in the dynamical behavior

Abstract

In this work we consider Randall-Sundrum braneworld type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behaviour of Friedmann-Lemaitre-Robertson-Walker type models, whose matter is described by a scalar field with an exponential potential. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, in particular, what new critical points appear and their nature and the occurrence of bifurcation.