Self-interacting Scalar Field Trapped in a Randall-Sundrum Braneworld: The Dynamical Systems Perspective

Details Self-interacting Scalar Field Trapped in a Randall-Sundrum Braneworld: The Dynamical Systems Perspective Self-interacting Scalar Field Trapped in a Randall-Sundrum Braneworld: The Dynamical Systems Perspective

2008-12-09

arxiv.org/abs/0812.1734v1

Phys.Lett.B676:161-167,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, 14 eps figures

Scientific paper

10.1016/j.physletb.2009.04.080

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a Randall-Sundrum brane. The simplest kinds of self-interaction potentials are investigated: a) constant potential, and b) exponential potential. It is shown that the dynamics of the Randall-Sundrum model significantly differs from the standard four-dimensional behavior at early times: in all cases of interest the (singular) empty universe is the past attractor for every trajectory in phase space, meanwhile the kinetic energy-dominated solution is always a saddle critical point. The late-time dynamics is not affected by the brane effects.

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