Accelerating Cosmologies from Exponential Potentials

An exponential potential of the form $V\sim \exp(-2c \phi/M_p)$ arising from the hyperbolic or flux compactification of higher-dimensional theories is of interest for getting short periods of accelerated cosmological expansions. Using a similar potential but derived for the combined case of hyperbolic-flux compactification, we study the four-dimensional flat (and open) FLRW cosmologies and give analytic (and numerical) solutions with exponential behavior of scale factors. We show that, for the M-theory motivated potentials, the cosmic acceleration of the universe can be eternal if the spatial curvature of the 4d spacetime is negative, while the acceleration is only transient for a spatially flat universe. We also comment on the size of the internal space and its associated geometric bounds on massive Kaluza-Klein excitations.Comment: 17 pages, 6 figures; minor typos fixe

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 ~ e^{-\mu\phi} 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 \Omega_{m}, w_{\phi} provide, independently of initial conditions and other parameters, necessary conditions on \mu. Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w_{\phi} ~ -1, as well as, for the generic late-times evolution, the general relation \Omega_{\phi}(w_{\phi}) is obtained.Comment: RevTex4, 9 pages, 2 figures, References adde