Large Logarithms from Quantum Gravitational Corrections to a Massless, Minimally Coupled Scalar on de Sitter

TL;DR

This paper investigates quantum gravitational effects on a massless scalar in de Sitter space, revealing large logarithmic corrections over time and space, with implications for gauge dependence in quantum gravity.

Contribution

It demonstrates the presence of large logarithms from graviton loops and discusses how to address gauge dependence in quantum gravitational corrections.

Findings

Large temporal logarithm in scalar field evolution.

Large spatial logarithm in scalar potential at large distances.

Potential for renormalization group interpretation of corrections.

Abstract

We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results set the stage for a project to purge gauge dependence by including quantum gravitational corrections to the source which disturbs the effective field and to the observer who measures it.