Large logarithms from quantum gravitational corrections to a massless, minimally coupled scalar on de Sitter

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.

How Inflationary Gravitons Affect the Force of Gravity

“…In Step 3, we first combine T i N (x; x ) with the remainder ∆T i L (x; x ). For our example of T 12 (x; x ), we add (35) and (42),…”

“…We therefore conclude that loops of inflationary gravitons contribute more strongly than matter loops by two large logarithms. It is also noteworthy that graviton loop corrections to gravity are much stronger than graviton loop corrections to fermions [25][26][27], to electrodynamics [28][29][30][31][32], and to massless, minimally coupled scalars [33][34][35]. The key difference seems to be that graviton loop corrections to gravity can involve two graviton propagators, whereas graviton corrections to other fields involve only one.…”

How Inflationary Gravitons Affect the Force of Gravity

“…A procedure has been developed for removing this gauge dependence [42], which has been successfully applied on flat space background to graviton loop corrections to the massless, minimally coupled scalar [42], and to electromagnetism [43]. The massless, minimally coupled scalar exchange potential ha been identified as the simplest venue for generalizing this technique to de Sitter background [36], and it is hoped that a result will be available later this year. Based on flat space background experience [42,43], we expect that the elimination of gauge dependence will not eliminate large graviton logarithms but might change their numerical coefficients.…”

“…We therefore conclude that loops of inflationary gravitons contribute more strongly than matter loops by two large logarithms. It is also noteworthy that graviton loop corrections to gravity are much strong than graviton loop corrections to fermions [26][27][28], to electrodynamics [29][30][31][32][33], and to massless, minimally coupled scalars [34][35][36]. The key difference seems to be that graviton loop corrections to gravity can involve two graviton propagators whereas graviton corrections to other fields involve only one.…”

“…This speculation was recently confirmed in the context of nonlinear sigma models on a nondynamical de Sitter background [40], which possess the same kinds of derivative interactions as quantum gravity and exhibit the same mixture of "tail" and ultraviolet logarithms. The technique has been applied to explain graviton loop corrections to the exchange potential of a massless, minimally coupled scalar [36], and strenuous efforts are underway to devise similar explanations for the collection of large graviton logarithms that have been patiently accumulated by direct computation over the course of two decades.…”