How round is the quantum de Sitter universe?

TL;DR

This paper explores the local geometric properties of a quantum universe generated by Causal Dynamical Triangulations, finding evidence that it resembles a four-sphere, supporting its interpretation as a de Sitter space.

Contribution

It introduces a new quantum curvature observable to analyze local geometry in nonperturbative quantum gravity, confirming de Sitter-like properties at large scales.

Findings

Quantum Ricci curvature matches four-sphere behavior at large scales

Supports de Sitter universe emergence in CDT quantum gravity

Strengthens semiclassical interpretation of quantum spacetime

Abstract

We investigate the quantum Ricci curvature, which was introduced in earlier work, in full, four-dimensional quantum gravity, formulated nonperturbatively in terms of Causal Dynamical Triangulations (CDT). A key finding of the CDT approach is the emergence of a universe of de Sitter-type, as evidenced by the successful matching of Monte Carlo measurements of the quantum dynamics of the global scale factor with a semiclassical minisuperspace model. An important question is whether the quantum universe exhibits semiclassicality also with regard to its more local geometric properties. Using the new quantum curvature observable, we examine whether the (quasi-)local properties of the quantum geometry resemble those of a constantly curved space. We find evidence that on sufficiently large scales the curvature behaviour is compatible with that of a four-sphere, thus strengthening the interpretation of the dynamically generated quantum universe in terms of a de Sitter space.