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

TL;DR

This paper uses dynamical systems methods to analyze the behavior of a self-interacting scalar field on a Randall-Sundrum brane, revealing early-time differences from standard cosmology and consistent late-time dynamics.

Contribution

It applies dynamical systems analysis to scalar fields on Randall-Sundrum branes with specific potentials, highlighting differences from four-dimensional models.

Findings

Early universe dynamics differ from standard models due to brane effects.

Empty universe acts as a past attractor in phase space.

Late-time behavior remains unaffected by brane effects.

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.