Qualitative Analysis of Brans-Dicke Universes with a Cosmological Constant

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 $γ$-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 $(ω> 0)$, 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&#39;&#39; universes, ``vacillating&#39;&#39; 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 appear to offer any advantage over the standard deSitter solution of general relativity in achieving a graceful exit from inflation.