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

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.

v1: 15 pages; v2: shortened to 10 pages, main results unchanged, published in Class. Quant. Grav

References in corpus (11)

• Exact evolution equation for the effective potential
• Towards singularity and ghost free theories of gravity
• Effective Action of Vacuum: Semiclassical Approach
• Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario
• Inflationary solutions in asymptotically safe f(R) theories
• An effective action for asymptotically safe gravity
• A short introduction to asymptotic safety
• Stable Isotropic Cosmological Singularities in Quadratic Gravity
• Renormalisation group improvement of scalar field inflation
• Evolution of cosmological perturbations in an RG-driven inflationary scenario
• f(R) Gravity from the renormalisation group

Cited by in corpus (28)

• Quasinormal modes of scale dependent black holes in (1+2)-dimensional Einstein-power-Maxwell theory
• Black holes within Asymptotic Safety
• Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem
• Scale dependent three-dimensional charged black holes in linear and non-linear electrodynamics
• A scale dependent black hole in three-dimensional space-time
• From renormalization group flows to cosmology
• Scale-dependent (2+1) - dimensional electrically charged black holes in Einstein-power-Maxwell theory
• Can scale-dependent cosmology alleviate the $H_0$ tension?
• Scale Setting for Self-consistent Backgrounds
• Scale-dependent rotating BTZ black hole
• Formation and evaporation of quantum black holes from the decoupling mechanism in quantum gravity
• Black Holes in Asymptotically Safe Gravity
• Brans-Dicke theory in the local potential approximation
• Cosmological constant problem: deflation during inflation
• Tensor instabilities at the end of the LCDM universe
• Scalar-Tensor gravity with system-dependent potential and its relation with Renormalization Group extended General Relativity
• On the cutoff identification and the quantum improvement in asymptotically safe gravity
• On the traversability of wormhole solutions in asymptotically safe gravity
• Scale-invariance at the core of quantum black holes
• Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
• Preliminary test of cosmological models in the scale-dependent scenario
• The effects of running gravitational coupling on three dimensional black holes
• Generalized Ellis-Bronnikov wormholes in asymptotically safe gravity
• Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
• A technique for natural gauge boson masses
• Vacuum energy, the Casimir effect, and Newton's non-constant
• Equivalence of scalar-tensor theories and scale-dependent gravity
• A Universe from a Lagrangian Fixed Point