Dagoberto Escobar, Carlos R. Fadragas, Genly Leon, Yoelsy Leyva
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. Using the center manifold theory we obtain sufficient
conditions for the asymptotic stability of de Sitter solution with standard 4D
behavior. We also prove that there are not late time de Sitter attractors with
5D-modifications since they are always saddle-like. This fact correlates with a
transient primordial inflation. We present here sufficient conditions on the
potential for the stability of the scalar field-matter scaling solution, the
scalar field-dominated solution, and the scalar field-dark radiation scaling
solution. We illustrate our analytical findings using a simple $f$-deviser as a
toy model. All these results are generalizations of our previous results
obtained for FRW branes.
View original:
http://arxiv.org/abs/1201.5672
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