Renormalization group improved gravitational actions: a Brans-Dicke approach

TL;DR

This paper introduces a novel approach to quantum gravity where the renormalization group influences the gravitational action, leading to a dynamic, scalar-field-like behavior of Newton's constant and the cosmological constant within a Brans-Dicke framework.

Contribution

It develops a new RG-improved gravitational model with scalar functions for G and Lambda, analyzing their dynamics and energy-momentum in a Brans-Dicke-like setting, especially in cosmology.

Findings

G and Lambda are dynamical and carry energy-momentum.

The model is consistent with a Brans-Dicke type effective Einstein equation.

The fixed point regime of the RG flow is thoroughly analyzed.

Abstract

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.