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