Self accelerating solutions in a DGP brane with a scalar field trapped on it: the dynamical systems perspective

TL;DR

This paper uses dynamical systems analysis to explore the behavior of a scalar field on a DGP brane, revealing complex dynamics and screening effects that depend on the potential type, with implications for cosmological models.

Contribution

It applies dynamical systems methods to analyze scalar field dynamics on a DGP brane, highlighting potential-dependent screening phenomena and stability properties.

Findings

Screening of scalar potential occurs as an attractor for constant potential.

Exponential potential does not exhibit gravitational screening as a critical point.

DGP models show rich and complex dynamical behavior.

Abstract

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a DGP brane. The simplest kinds of self-interaction potentials are investigated: a) constant potential, and b) exponential potential. It is shown that the dynamics of DGP models can be very rich and complex. One of the most interesting results of this study shows that dynamical screening of the scalar field self-interaction potential, occuring within the Minkowski cosmological phase of the DGP model and mimetizing 4D phantom behaviour, is an attractor solution for a constant self-interaction potential but not for the exponential one. In the latter case gravitational screening is not even a critical point of the corresponding autonomous system of ordinary differential equations.