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 φ of exponential potential V(φ) ∼ exp(-μφ) plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation for Ωφ(wφ) or q(wφ), 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 μ, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints Ωm0 ∼ 0.25 - 0.3, -1 ≤ wφ0 ≤ -0.6, provides, independently of initial conditions and other parameters, the necessary condition 0 < μ < or approx. 1.6√8πGN, while the less conservative constraint -1 ≤ wφ ≤ -0.93 gives 0 < μ < or approx. 0.7√8πGN. Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case wφ ∼ -1, the general relation Ωφ(wφ) is obtained. The generic (nonlinearized) late-times solution of the system in the plane (wφ, Ωφ) or (wφ, q) is also derived