On the running of the gravitational constant

TL;DR

The paper argues that defining a universal running gravitational constant G(E) below the Planck scale is problematic due to highly variable quantum corrections, challenging the concept's applicability.

Contribution

It demonstrates that quantum corrections to gravity do not behave like a typical running coupling, questioning the validity of G(E) in this regime.

Findings

Quantum corrections vary greatly in magnitude and sign.

No consistent universal G(E) can be defined in the perturbative regime.

Results pose challenges for the Asymptotic Safety program.

Abstract

We show that there is no useful and universal definition of a running gravitational constant, G(E), in the perturbative regime below the Planck scale. By consideration of the loop corrections to several physical processes, we show that the quantum corrections vary greatly, in both magnitude and sign, and do not exhibit the required properties of a running coupling constant. We comment on the potential challenges of these results for the Asymptotic Safety program.