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 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.