Qualitative analysis of Brans-Dicke universes with a cosmological constant.

Solutions to flat space Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory with a cosmological constant are investigated. The matter is modeled as a γ-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 to (ω > 0), all initially expanding models approach exponential expansion at late times, regardless of the type of matter present. If ω > 0, then a wide variety of qualitatively distinct models are present, including nonsingular "bounce" universes, "vacillating" universes, and, in the special case of ω = -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 appears to offer any advantage over the standard de Sitter solution of general relativity in achieving a graceful exit from inflation.