Self-interacting scalar field trapped in a Randall–Sundrum braneworld: The dynamical systems perspective

Abstract

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.