Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis

TL;DR

This paper analyzes a massless scalar field with self-interaction during inflation, comparing quantum field theory and stochastic methods, and finds consistent results showing how correlations evolve over time and space.

Contribution

It provides a detailed quantum and stochastic analysis of scalar field correlations during inflation, including loop corrections and their effects on variance and correlation growth.

Findings

Tree-order correlator freezes at a nonzero value

One-loop correction causes negative growth in correlations

Quantum and stochastic analyses yield consistent results

Abstract

We consider an infrared truncated massless minimally coupled scalar field with a quartic self-interaction in the locally de Sitter background of an inflating universe. We compute the two-point correlation function of the scalar at one and two-loop order applying quantum field theory. The tree-order correlator at a fixed comoving separation (that is at increasing physical distance) freezes in to a nonzero value. At a fixed physical distance, it grows linearly with comoving time. The one-loop correlator, which is the dominant quantum correction, implies a negative temporal growth in the correlation function, at this order, at a fixed comoving separation and at a fixed physical distance. We also obtain quantitative results for variance in space and time of one and two-loop correlators and infer that the contrast between the vacuum expectation value and the variance becomes less pronounced when the loop corrections are included. Finally, we repeat the analysis of the model applying a stochastic field theory and reach the same conclusions.