Renormalization Group-Improved Gravitational Action: A Lagrangian Framework

TL;DR

This paper introduces a novel Lagrangian-based approach to incorporate the renormalization group running of Newton's constant and the cosmological constant into gravity, leading to a new class of modified gravity theories with spacetime-dependent G and Lambda.

Contribution

It develops a Lagrangian framework for quantum-inspired scale dependence of G and Lambda, connecting with Horndeski gravity and exploring cosmological solutions.

Findings

Non-singular power-law inflation solution identified

Framework can generate scalar and tensor perturbations

Links quantum effects to modified gravity dynamics

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 $\Lambda$ are spacetime-dependent functions. The Lagrangian formulation can be interpreted as an effective gravitational action that encapsulates the scale dependence of $G$ and $\Lambda$, 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.