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 phi of exponential potential V(phi) similar to exp(-muphi) plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation for Omega(phi) (w(phi)) or q(w(phi)), 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 mu, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints Omega(m0) approximate to 0.25 - 0.3, -1 less than or equal to, w(phi0) less than or equal to, -0.6, provides, independently of initial conditions and other parameters, the necessary condition 0 < mu less than or similar to 1.6 root8piG(N), while the less conservative constraint -1 less than or equal to w(phi) less than or equal to -0.93 gives 0 < mu less than or equal to 0.7root8piG(N). Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case wphi approximate to -1, the general relation Omega(phi)(wphi) is obtained. The generic (nonlinearized) late-times solution of the system in the plane (w(phi), Omega(phi)) or (w(phi), q) is also derived.