Stochastic ultra slow roll inflation

Abstract

We study the ultra slow roll model in the context of stochastic inflation.\nUsing stochastic $\\delta N$ formalism, we calculate the mean number of\n$e$-folds, the power spectrum, the bispectrum and the stochastic corrections\ninto these observables. We reproduce correctly the known leading classical\ncontributions to these cosmological observables while we show that the\nfractional corrections to cosmological observables induced from stochastic\ndynamics are at the order of power spectrum. In addition, we consider a\nhypothetical setup containing two absorbing barriers on both sides of the field\nconfiguration and calculate the probability of first boundary crossing\nassociated with the classical motion and quantum jumps. This analysis includes\nthe limit of Brownian motion of the quantum fluctuations of a test scalar field\nin a dS spacetime.\n