New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann--Robertson--Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour with p>1, while another class exhibits a late time approach to the behaviour of the coasting models. Bouncing models are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided.
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Crawford et al. (1994) studied this question.
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