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

Accelerating cosmologies from exponential potentials