Cosmology with exponential potentials

Abstract

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 ϕof exponential potential ~ e^{-μϕ} plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation, 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, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints on the present values of Ω_{m}, w_ϕ provide, independently of initial conditions and other parameters, necessary conditions on μ. Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w_ϕ ~ -1, as well as, for the generic late-times evolution, the general relation Ω_ϕ(w_ϕ) is obtained.