Combining the stochastic and $$\delta N$$δN formalisms, we derive non-perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime, we show that a strong suppression in the power spectrum is generically obtained, and we comment on the physical implications of this effect.
CITATION STYLE
Vennin, V., & Starobinsky, A. A. (2015). Correlation functions in stochastic inflation. European Physical Journal C, 75(9). https://doi.org/10.1140/epjc/s10052-015-3643-y
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