Quantum Effects of Mass on Scalar Field Correlations and Fluctuations during Inflation

TL;DR

This paper analyzes how mass influences quantum fluctuations of a scalar field during inflation, showing that mass suppresses growth of correlations and fluctuations compared to the massless case, with detailed loop calculations.

Contribution

It provides an analytical computation of scalar field correlations and fluctuations during inflation, including quantum loop corrections, highlighting the suppressive effect of mass on growth of correlations.

Findings

Mass suppresses late-time growth of correlations.

Quantum corrections reduce the variance of field fluctuations.

Massive fields show asymptotic behavior different from massless fields.

Abstract

We consider an infrared truncated massive 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 and the mean squared fluctuations (variance) of the field variation analytically, at tree, one- and two-loop order. The one-loop correlator at a fixed comoving separation asymptotes to zero in the massive case but grows, at late times, like $-\lambda\ln^2(a)$ in the massless limit, where $a$ is the cosmic scale factor. For a fixed physical distance, on the other hand, it grows, at late times, like $-\lambda\ln^3(a)$ in the massless limit. This growth is severely suppressed in the massive case. In fact, the one-loop correlator asymptotes effectively to zero for masses larger than half the expansion rate. We find out also that the tree-order variance of field variation decreases when quantum corrections are included. Hence, the actual effect that any local observer perceives in the field strength as fluctuations happen does not deviate from the average effect as much as the tree-order variance implies.