CURVATURE AND FLATNESS IN A BRANS-DICKE UNIVERSE

The evolution of a universe with Brans-Dicke gravity and nonzero curva ture is investigated here. We find solutions to the equations of motio n during the radiation dominated era. In a Friedman-Robertson-Walker c osmology we show explicitly that the three possible values of curvatur e kappa = + 1, 0, - 1 divide the evolution of the Brans-Dicke universe into dynamically distinct classes just as for the standard model. Sub sequently we discuss the flatness problem which exists in Brans-Dicke gravity as it does in the standard model. We also demonstrate a flatne ss problem in MAD Brans-Dicke gravity. In general, in any model that a ddresses the horizon problem, including inflation, there are two compo nents to the flatness issue: (i) at the Planck epoch curvature gains i mportance, and (ii) during accelerated expansion curvature becomes les s important and the universe flattens. In many cases the universe must be very flat at the Planck scale in order for the accelerated epoch t o be reached; thus there can be a residual flatness problem.