Scalar field quantum fluctuations and fine-tuning in chaotic inflationary models

During chaotic inflation, the dispersion of a scalar field can show interesting nonlinear effects. This is not seen in treatments which combine a deterministic description for the mean-field evolution with a diffusion approximation for the quantum fluctuations. We derive a criterion which distinguishes the diffusive regime from the nonlinear regime using stochastic dynamics in models of noninteracting multiple scalar fileds. In the nonlinear regime, dispersion estimates based on a simple diffusion approximation fail due to a strong nonlinear drift effect. We give some simple numerical examples to support this result. We apply our results to a double inflation model and show that estimates of the probability of successful inflation depend on a correct treatment of nonlinear effects. Including them greatly reduces the amount of fine-tuning necessary in this model.