Renormalization Group-Improved Gravitational Action: A Lagrangian Framework

TL;DR

This work develops a covariant, local action that encodes the renormalization group running of Newton's constant and the cosmological constant within an asymptotically safe gravity framework. By introducing a non-dynamical RG-flow scalar $\psi$ and a running $G$ entering the matter sector, the authors derive modified Einstein equations that respect diffeomorphism invariance and reproduce the RG-improved dynamics. They analyze quantum cosmology and cosmological evolution under two scale-identifications, $k\propto 1/t$ and $k\propto H$, obtaining non-singular, power-law inflationary solutions near fixed points and deriving the corresponding tensor and scalar perturbation spectra using a Horndeski-like mapping. The results yield predictions for the primordial spectra, tensor-to-scalar ratio, and spectral indices that can be confronted with observations, while maintaining a local, dynamical-consistent description without extra propagating degrees of freedom.

Abstract

A new approach for embedding the renormalization group running of Newton's constant and cosmological constant in gravity is proposed. This approach is based on a gravitational Lagrangian that gives rise to a new class of modified gravity theories where $G$ and $Λ$ are spacetime-dependent functions. The Lagrangian formulation can be interpreted as an effective gravitational action that encapsulates the scale dependence of $G$ and $Λ$, arising from quantum effects in the early universe. We show that the new formalism can be discussed using partially the framework and results of Horndeski modified gravity, excluding the equations of motion of the scalar field. The study explores aspects of this new gravity action. We also analyze an interesting non-singular cosmological solution featuring power-law inflation and we discuss the generation of scalar and tensor perturbations within this framework.