Can all the infrared secular growth really be understood as increase of classical statistical variance?

TL;DR

This paper investigates whether the infrared growth of correlations during inflation can be fully understood as an increase in classical statistical variance, by deriving an effective stochastic description of long-wavelength scalar field modes.

Contribution

It provides a refined derivation of the effective action for IR modes and demonstrates their evolution can be interpreted as a classical stochastic process.

Findings

Effective EoM reproduces IR correlation functions accurately at late times.

IR modes can be modeled as a classical stochastic process.

The approach clarifies the physical meaning of IR enhancement in inflation.

Abstract

It is known that in the theory of light scalar fields during inflation, correlation functions suffer from infrared (IR) divergences or large IR loop corrections, leading to the breakdown of perturbation theory. In order to understand the physical meaning of such IR enhancement, we investigate the stochastic properties of an effective equation of motion (EoM) for long-wavelength modes of a canonically normalized light scalar field $\phi$ with a general sufficiently flat interaction potential on de Sitter background. Firstly, we provide an alternative refined derivation of the effective action for long-wavelength modes which leads to the effective EoM that correctly reproduces all the IR correlation functions in a good approximation at a late time, by integrating out short-wavelength modes. Next, under the assumption that one can neglect non-local correlations in the influence functional exceeding the coarse-graining scale, we show that the effective EoM for IR modes of the "average field" in Schwinger-Keldysh formalism $\phi^<_c$ can be interpreted as a classical stochastic process in the present model.