Stochastic Inflation and Replica Field Theory

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We formulate a general replica field-theoretic framework for stochastic inflation in which a manifestation of dimensional reduction is found. The scale above which the latter becomes dominant is explicitly calculated. It is found that for a wide class of stochastic systems considerable changes of the spectral index inevitably occur on super-horizon scales. We work out an explicit relation between the noise correlator and the non-Gaussianity parameter $f_{NL}$, which thus can effectively be generated entirely by quantum fluctuations.