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

Understand

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 $R$.