Bimetric Renormalization Group Flows in Quantum Einstein Gravity

TL;DR

This paper develops a bimetric approach to the functional renormalization group in Quantum Einstein Gravity, revealing a new fixed point and confirming the stability of the Asymptotic Safety scenario.

Contribution

It introduces the first comprehensive study of the full bimetric gravitational RG flow, including mixed interactions, and identifies a new fixed point affecting IR behavior.

Findings

The Asymptotic Safety fixed point remains stable with bimetric interactions.

A new fixed point emerges when mixed metric terms are included.

The bimetric structure influences the IR dynamics of quantum gravity.

Abstract

The formulation of an exact functional renormalization group equation for Quantum Einstein Gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of "background independence" is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the Asymptotic Safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory's IR behavior.