One-loop Graviton Corrections to Conformal Scalars on a de Sitter Background

TL;DR

This paper calculates one-loop graviton corrections to a conformally coupled scalar in de Sitter space, showing no large infrared effects but revealing a decaying logarithmic correction and short-distance running of the potential.

Contribution

It provides the first detailed quantum correction analysis of conformal scalars on de Sitter space including graviton loops, with implications for infrared behavior.

Findings

No large infrared logarithms in mode functions or response to sources.

Presence of a decaying logarithmic correction to the mode function.

Short-distance logarithmic running of the scalar potential.

Abstract

We exploit a recent computation of one graviton loop corrections to the self-mass [1] to quantum-correct the field equation for a massless, conformally coupled scalar on a de Sitter background. With the obvious choice for the finite part of the $R^2 \phi^2$ counterterm, we find that neither plane wave mode functions nor the response to a point source acquires large infrared logarithms. However, we do find a decaying logarithmic correction to the mode function and a short distance logarithmic running of the potential in addition to the power-law effect inherited from flat space.