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The effects of thermal fluctuations on the evolution of a weakly coupled scalar field in the preinflationary phase of a model of new inflation are studied. Limits on the coupling constants are derived below which the effects of thermal fluctuations are negligible. The stochastic approach to inflation is extended to cover a situation in which spatial gradient terms and acceleration terms in the equation of motion of the scalar field dominate.
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Brandenberger et al. (1988) studied this question.
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