Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety

TL;DR

This paper investigates bimetric truncations within the average action approach to quantum gravity, exploring their implications for asymptotic safety and the cosmological constant problem, using conformally reduced gravity as a simplified model.

Contribution

It introduces a first nontrivial bimetric truncation in conformally reduced gravity, addressing conceptual issues and potential impacts on quantum gravity research.

Findings

Truncated flow equations show trivial background dependence so far.

First nontrivial bimetric truncation analyzed in conformally reduced gravity.

Implications for asymptotic safety and the cosmological constant are discussed.

Abstract

In the average action approach to the quantization of gravity the fundamental requirement of "background independence" is met by actually introducing a background metric but leaving it completely arbitrary. The associated Wilsonian renormalization group defines a coarse graining flow on a theory space of functionals which, besides the dynamical metric, depend explicitly on the background metric. All solutions to the truncated flow equations known to date have a trivial background field dependence only, namely via the classical gauge fixing term. In this paper we analyze a number of conceptual issues related to the bimetric character of the gravitational average action and explore a first nontrivial bimetric truncation in the simplified setting of conformally reduced gravity. Possible implications for the Asymptotic Safety program and the cosmological constant problem are discussed in detail.