Exponential Potentials on the Brane

TL;DR

This paper investigates how the presence of the five-dimensional Weyl tensor influences the cosmological dynamics of brane-world models with exponential potentials, highlighting differences from standard general relativity.

Contribution

It introduces a dynamical systems analysis of scalar field cosmologies on the brane considering Weyl tensor effects, extending previous models without this contribution.

Findings

Weyl tensor modifies the phase space structure of cosmological models.

New stable and unstable solutions emerge due to Weyl tensor effects.

Differences from standard GR and Weyl-free brane scenarios are characterized.

Abstract

In this paper we study the cosmological dynamics of Randall-Sundrum braneworld type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined. Using dynamical systems techniques, we study how the state space of Friedmann-Lemaitre-Robertson-Walker (FLRW) and Bianchi type I scalar field models with an exponential potential is affected by the bulk Weyl tensor, focusing on the differences that appear with respect to standard general relativity and also Randall-Sundrum cosmological scenarios without the Weyl tensor contribution.