Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-10-08
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, 8 figures, one author added, the discussion in section III have been improved and enlarged
Scientific paper
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 pefect 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).
Escobar Dagoberto
Fadragas Carlos R.
Leon Genly
Leyva Yoelsy
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