Self Regulation of Infrared Correlations for Massless Scalar Fields during Inflation

TL;DR

This paper calculates the self-energies of a scalar field with interactions in de Sitter space, showing how loop corrections induce a dynamical mass that self-regulates infrared divergences.

Contribution

It provides a comprehensive calculation of the self-energy contributions from quartic and trilinear interactions, establishing a self-consistent dynamical mass in de Sitter space.

Findings

Effective mass arises from seagull and sunset diagrams.

Trilinear interactions also generate a dynamical mass.

Infrared divergences are naturally self-regulated by these loop effects.

Abstract

Self-energies of a minimally coupled scalar field with quartic and trilinear interactions are calculated in a de Sitter background, using a position space propagator. For quartic interactions, we recover earlier results for the seagull diagram, namely that it contributes an effective mass for the scalar field at leading order in the infrared enhancement in a steady-state de Sitter background. We further show that the sunset diagram also contributes to this effective mass and argue that these two contributions are sufficient in order to determine a self-consistent dynamical mass. In addition, trilinear interactions also induce a dynamical mass for the scalar field which we calculate. Since an interacting scalar field in de Sitter acquires a dynamical mass through these loop corrections, the infrared divergences of the two-point correlator are naturally self-regulated.