Stochastic analysis of the initial condition constraints on chaotic inflation

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Abstract
We use stochastic dynamics to examine the probability of successful inflation from various initial conditions at the Planck epoch. This approach allows us to approximate the effect of strong quantum fluctuations at the earliest epoch of inflation, including fluctuations in the local expansion rate. The wellknown classical attractors along the slow-roll trajectory exist even when large quantum fluctuations in the early Planck epoch are included. However, our results suggest that a significant fraction of the initial condition phase space which leads to a successful inflationary stage in the classical analysis actually fails to inflate.