Phase space analysis of quintessence fields trapped in a Randall-Sundrum braneworld: a refined study

TL;DR

This paper analyzes the stability and evolution of scalar fields in a Randall-Sundrum braneworld using dynamical systems, revealing conditions for stable solutions and the transient nature of primordial inflation.

Contribution

It provides a refined dynamical systems analysis of quintessence fields in Randall-Sundrum braneworlds, including stability conditions and the non-existence of late-time attractors with 5D modifications.

Findings

De Sitter solutions can be stable or unstable depending on potential parameters.

No late-time attractors with 5D modifications, indicating transient primordial inflation.

Stability conditions depend on the scalar field potential and parameters.

Abstract

In this paper we investigate, from the dynamical systems perspective, the evolution of an scalar field with arbitrary potential trapped in a Randall-Sundrum's Braneworld of type II. We consider an homogeneous and isotropic Friedmann-Robertson-Walker (FRW) brane filled also with a perfect fluid. Center Manifold Theory is employed to obtain sufficient conditions for the asymptotic stability of de Sitter solution. We obtain conditions on the potential for the stability of scaling solutions as well for the stability of the scalar-field dominated solution. We prove the there are not late time attractors with 5D-modifications (they are saddle-like). This fact correlates with a transient primordial inflation. In the particular case of a scalar field with potential $V=V_{0}e^{-\chi\phi}+\Lambda$ we prove that for $\chi<0$ the de Sitter solution is asymptotically stable. However, for $\chi>0$ the de Sitter solution is unstable (of saddle type).