Quantum Curvature as Key to the Quantum Universe

TL;DR

This paper discusses a novel approach to defining and using quantum Ricci curvature in nonperturbative quantum gravity, particularly within Causal Dynamical Triangulations, to better understand quantum spacetime geometry.

Contribution

It introduces a new quantum Ricci curvature concept applicable to piecewise flat triangulations, enabling the study of quantum geometry without smooth structures.

Findings

Quantum Ricci curvature exists and is useful in CDT models.

QRC behaves consistently in classical and quantum regimes.

Potential to connect quantum gravity with observable gravitational phenomena.

Abstract

Curvature is a key notion in General Relativity, characterizing the local physical properties of spacetime. By contrast, the concept of curvature has received scant attention in nonperturbative quantum gravity. One may even wonder whether in a Planckian regime meaningful notions of (quantum) curvature exist at all. Remarkably, recent work in quantum gravity using Causal Dynamical Triangulations (CDT) has demonstrated both the existence and usefulness of a new notion of quantum Ricci curvature (QRC), which relies neither on smooth structures nor on tensor calculus. This overview article recalls some classical notions related to curvature and parallel transport, as well as previous unsuccessful attempts to construct quantum curvature observables based on deficit angles and Wilson loops. It introduces the quasi-local QRC on piecewise flat triangulations, and describes its behaviour in a purely classical setting, its use in quantum observables, and currently known results in (C)DT quantum gravity in two and four dimensions. The QRC opens the door to a range of interesting physical observables that were previously out of reach, and will help to bridge the gap between the nonperturbative quantum theory and gravitational phenomena at lower energies.