Renormalization group flow of f(R)-gravity

Abstract

We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The non-perturbative RG flow of non-local extensions of the Einstein-Hilbert truncation including $\int d^dx \sqrt{g} \ln(R)$ and $\int d^dx \sqrt{g} R^{-n}$ interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some $R^{-n}$-truncations all physical trajectories emanate from a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the $\ln(R)$-truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.