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A Fokker-Planck equation that accounts for fluctuations in field and its conjugate momentum is solved numerically for the case of a λϕ 4 potential. Although the amount of inflation agrees closely with that expected classically, in certain cases (large initial fields or large dispersions) the "slow rolling" approximation appears invalid. In such cases inflation would stop prematurely before possibly restarting.
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Coule et al. (1987) studied this question.
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