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Abstract

It is shown that spatially homogeneous solutions of the Einstein equations coupled to a nonlinear scalar field and other matter exhibit accelerated expansion at late times for a wide variety of potentials V. These potentials are strictly positive but tend to zero at infinity. They satisfy restrictions on V'/V and V"/V' related to the slow-roll approximation. These results generalize Wald's theorem for spacetimes with positive cosmological constant to those with accelerated expansion driven by potentials belonging to a large class.