Dynamics of a Self-interacting Scalar Field Trapped in the Braneworld for a Wide Variety of Self-interaction Potentials

TL;DR

This paper uses dynamical systems analysis to explore how a self-interacting scalar field behaves in two braneworld models, revealing deviations from standard general relativity at different scales.

Contribution

It provides a comparative analysis of scalar field dynamics in RS and DGP braneworlds using phase space methods, highlighting their distinct modifications to gravity.

Findings

RS model introduces UV corrections to general relativity.

DGP model causes IR modifications at large scales.

Scalar field dynamics differ significantly from standard GR behavior.

Abstract

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped in the braneworld, for a wide variety of self-interaction potentials. We focus on Randall-Sundrum (RS) and on Dvali-Gabadadze-Porrati (DGP) braneworld models exclusively. These models are complementary to each other: while the RS brane produces ultra-violet (UV) corrections to general relativity, the DGP braneworld modifies Einstein's theory at large scales, i. e., produces infra-red (IR) modifications of general relativity. This study of the asymptotic properties of both braneworld models, shows -- in the phase space -- the way the dynamics of a scalar field trapped in the brane departs from standard general relativity behaviour.