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The authors consider exact cosmological solutions of the Einstein gravitational equations with a non-interacting combination of a classical scalar field and isotropic radiation as source. They show how a potential function for the scalar field can be found leading to desired volume behaviour of Robertson-Walker universes, and give a number of exact solutions of the coupled equations. These solutions in general do not obey the 'slow-rolling' approximation usually assumed in inflationary universe models.
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Ellis et al. (1991) studied this question.
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