# Correlation functions in stochastic inflation

Vincent Vennin, Alexei A. Starobinsky

Research output: Contribution to journalArticlepeer-review

## Abstract

Combining the stochastic and $\delta N$ 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 comment on the physical implications of this effect.
Original language English 413 20 The European Physical Journal C 75 9 https://doi.org/10.1140/epjc/s10052-015-3643-y Published - 15 Jun 2015

• hep-th
• astro-ph.CO
• gr-qc
• hep-ph
• RCUK
• STFC
• ST/L005573/1

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