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In many cases a nonlinear scalar field with potential V can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for homogeneous spacetimes. It is shown that, under the assumption that V has a strictly positive minimum, Wald's theorem on spacetimes with positive cosmological constant can be generalized to a wide class of potentials. In some cases detailed information on late-time asymptotics is obtained. Results on the behaviour in the past time direction are also presented.doi:10.1088/0264-9381/21/9/018 fatcat:lxjy4c4imbgkrjy3fa3vraf4jy