Correlation functions in stochastic inflation

Vincent Vennin, Alexei A. Starobinsky

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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 languageEnglish
Article number413
Number of pages20
JournalThe European Physical Journal C
Issue number9
Publication statusPublished - 15 Jun 2015


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


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