Scale-dependent metric and causal structures in Quantum Einstein Gravity

TL;DR

This paper explores how the metric and causal structures in Quantum Einstein Gravity depend on scale, clarifying conceptual issues and proposing a notion of scale-dependent causality within the asymptotic safety framework.

Contribution

It introduces a detailed analysis of scale dependence in the metric and causality in Quantum Einstein Gravity, clarifying the role of scale-dependent diffeomorphisms and isometries.

Findings

Scale-dependent metrics are constructed within QEG.

A concept of scale-dependent causality is proposed and illustrated.

Differences between scale-dependent and independent symmetries are clarified.

Abstract

Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein Gravity (QEG) and the resulting families of resolution dependent metrics are discussed. The status of scale dependent vs. scale independent diffeomorphisms is clarified, and the difference between isometries implemented by scale dependent and independent Killing vectors is explained. A concept of scale dependent causality is proposed and illustrated by various simple examples. The possibility of assigning an "intrinsic length" to objects in a QEG spacetime is also discussed.