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

We present an autonomous phase-plane describing the evolution of FriedmannRobertson-Walker models containing a perfect fluid (with barotropic index γ) in BransDicke gravity (with Brans-Dicke parameter ω). 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 (ω, γ) parameter space for 0 ≤ γ ≤ 2 and ω > −3/2. We show that the condition for inflation in Brans-Dicke gravity is always stronger than the general relativistic condition, γ < 2/3.