Renormalization group scale-setting from the action - a road to modified gravity theories

TL;DR

This paper develops a method to set the renormalization group scale as a scalar field within gravitational actions, leading to insights into modified gravity theories and their cosmological implications.

Contribution

It extends the scale-setting procedure to various gravitational truncations, connecting RG corrections to effective $f(R)$ gravity and universal quadratic Ricci tensor actions.

Findings

Logarithmic RG dependence yields exponentially suppressed cosmological constant.

Scale-setting produces effective $f(R)$ theories with negative powers of $R$.

Universal quadratic Ricci tensor action emerges at the non-Gaussian fixed point.

Abstract

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the renormalization group is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG corrected gravitational theories yields the effective $f(R)$ modified gravity theories with negative powers of the Ricci scalar $R$. The scale-setting at the level of the action at the non-gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in Ricci tensor.