Cosmology with exponential potentials

We examine in the context of general relativity the dynamics of a spatially flat Robertson?Walker universe filled with a classical minimally coupled scalar field of exponential potential V() ~ exp(??) plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation for ?(w) or q(w), providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system for any value of ?, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints ?m0 ? 0.25 ? 0.3, ?1 ? w0 ? ?0.6, provides, independently of initial conditions and other parameters, the necessary condition , while the less conservative constraint ?1 ? w ? ?0.93 gives . Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w ? ?1, the general relation ?(w) is obtained. The generic (nonlinearized) late-times solution of the system in the plane (w, ?) or (w, q) is also derived.