Nonlocal Corrections to Scalar Field Effective Action in de Sitter spacetime

TL;DR

This paper studies quantum one-loop corrections to a scalar field in de Sitter spacetime, revealing nonlocal effects like memory and noise terms, and shows these corrections suppress field variance in the infrared.

Contribution

It introduces a comprehensive analysis of nonlocal quantum corrections in scalar fields on FLRW backgrounds, including derivation, renormalization, and physical implications.

Findings

Identification of nonlocal memory and noise terms in the effective action.

Renormalization of ultraviolet divergences in nonlocal structures.

Suppression of infrared field variance due to one-loop corrections.

Abstract

We investigate the one-loop effective action for a test scalar field in a general Friedmann-Lema\^itre-Robertson-Walker (FLRW) background, specifically focusing on quantum corrections up to the second order in the interaction strength. By employing the Schwinger-Keldysh formalism, we derive the equation of motion for the field expectation value, which incorporates not only the standard local radiative corrections but also novel nonlocal features: a memory term and a stochastic noise term. We identify all ultraviolet divergent structures within these nonlocal terms and provide a consistent renormalization procedure. To analyze the physical impact of these terms, we apply a local approximation under the assumption of slowly-varying fields, by which the memory term acts as a negative contribution to the drift coefficient. As a concrete application, we consider a massive $\phi^4$ theory and show that these one-loop corrections lead to a suppression of the field variance in the infrared regime compared to the tree-level results.