Phase-plane analysis of Friedmann-Robertson-Walker cosmologies in Brans-Dicke gravity

TL;DR

This paper analyzes the dynamics of Friedmann-Robertson-Walker cosmologies within Brans-Dicke gravity using phase-plane methods, identifying fixed points, stability conditions, and the impact on inflationary behavior.

Contribution

It introduces an autonomous phase-plane framework for Brans-Dicke cosmologies, characterizes fixed points, and explores stability and inflation conditions across parameter space.

Findings

Identifies self-similar fixed points corresponding to known solutions.

Derives conditions for stability of critical points.

Shows that Brans-Dicke inflation condition is more restrictive than in general relativity.

Abstract

We present an autonomous phase-plane describing the evolution of Friedmann-Robertson-Walker models containing a perfect fluid (with barotropic index gamma) in Brans-Dicke gravity (with Brans-Dicke parameter omega). We find self-similar fixed points corresponding to Nariai's power-law solutions for spatially flat models and curvature-scaling solutions for curved models. At infinite values of the phase-plane variables we recover O'Hanlon and Tupper's vacuum solutions for spatially flat models and the Milne universe for negative spatial curvature. We find conditions for the existence and stability of these critical points and describe the qualitative evolution in all regions of the (omega,gamma) parameter space for 0<gamma<2 and omega>-3/2. We show that the condition for inflation in Brans-Dicke gravity is always stronger than the general relativistic condition, gamma<2/3.