Cosmology in Brans-Dicke theory with a scalar potential

TL;DR

This paper analyzes the dynamics of cosmological models in Brans-Dicke theory with a scalar potential, revealing how self-interactions affect the phase space and evolution of different universe types.

Contribution

It provides a detailed phase space analysis of Brans-Dicke cosmologies with scalar potentials, highlighting differences from non-interacting dilaton models.

Findings

Radiation universe phase space is two-dimensional.

Dust and false vacuum universes have three-dimensional phase spaces.

Self-interacting scalar potential alters the dynamical behavior.

Abstract

We consider the general behaviour of cosmologies in Brans-Dicke theory where the dilaton is self-interacting via a potential $V(\Phi)$. We show that the general radiation universe is a two-dimensional dynamical system whereas the dust or false vacuum universe is three-dimensional. This is in contrast to the non-interacting dilaton which has uniformly a two-dimensional phase space. We find the phase spaces in each case and the general behaviour of the cosmologies.