Phase space analysis of quintessence fields trapped in a Randall-Sundrum Braneworld: anisotropic Bianchi I brane with a Positive Dark Radiation term

Understand

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 2.

• We consider an homogeneous but anisotropic Bianchi I (BI) brane filled also with a perfect fluid.
• We also consider the effect of the projection of the five-dimensional Weyl tensor onto the three-brane in the form of a positive Dark Radiation term.
• Using the center manifold theory we obtain sufficient conditions for the asymptotic stability of de Sitter solution with standard 4D behavior.