Qualitative Analysis of Brans-Dicke Universes with a Cosmological Constant

TL;DR

This paper analyzes flat Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory with a cosmological constant, revealing different late-time behaviors depending on the Brans-Dicke parameter, and finds no advantage over standard inflation models.

Contribution

It provides a qualitative dynamical systems analysis of Brans-Dicke cosmologies with a cosmological constant, highlighting the impact of the coupling constant on universe evolution.

Findings

For positive , models approach exponential expansion regardless of matter.

Negative  leads to diverse models including bounce and vacillating universes.

Power-law solutions are absent, offering no improvement over de Sitter inflation.

Abstract

Solutions to flat space Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory with a cosmological constant are investigated. The matter is modelled as a $\gamma$-law perfect fluid. The field equations are reduced from fourth order to second order through a change of variables, and the resulting two-dimensional system is analyzed using dynamical system theory. When the Brans-Dicke coupling constant is positive $(\omega > 0)$, all initially expanding models approach exponential expansion at late times, regardless of the type of matter present. If $\omega < 0$, then a wide variety of qualitatively distinct models are present, including nonsingular ``bounce'' universes, ``vacillating'' universes and, in the special case of $\omega = -1$, models which approach stable Minkowski spacetime with an exponentially increasing scalar field at late times. Since power-law solutions do not exist, none of the models appear to offer any advantage over the standard deSitter solution of general relativity in achieving a graceful exit from inflation.