Eur. Phys. J. C (2015) 75: 413
https://doi.org/10.1140/epjc/s10052-015-3643-y

Regular Article - Theoretical Physics

Correlation functions in stochastic inflation

¹ Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, UK
² L. D. Landau Institute for Theoretical Physics RAS, Moscow, 119334, Russian Federation
³ Department of Physics and Astronomy, Institute for Theoretical Physics, Utrecht University, 3508 TD, Utrecht, The Netherlands

^* e-mail: vincent.vennin@port.ac.uk

Received: 14 July 2015
Accepted: 26 August 2015
Published online: 9 September 2015

Abstract

Combining the stochastic and 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.