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Boundary Crossing in Stochastic Inflation with Critical Number of Fields
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We study boundary crossing probability in the context of stochastic inflation. We prove that for a generic multi-field inflationary potential, the probability that the inflaton reaches infinitely far regions in the field space is critically dependent on the number of fields, being nonzero for more than two fields, and zero otherwise. We also provide several examples where the boundary crossing probability can be calculated exactly, most notably, for a particular landscape of a two-field model with a multi-well potential.
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Deviations from Gaussian White Noise in Stochastic Inflation
Relaxing the sharp cutoff or the Bunch-Davies initial state in stochastic inflation makes the noise colored, and relaxing the initial state also makes it non-Gaussian.
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