Properties of dynamical fractal geometries in the model of Causal Dynamical Triangulations

TL;DR

This paper explores the fractal properties of quantum geometries in a universe modeled by Causal Dynamical Triangulations, revealing a semi-classical toroidal core with fractal outgrowths that dominate the volume.

Contribution

It provides new insights into the fractal and topological structure of quantum geometries within the Causal Dynamical Triangulations framework.

Findings

Quantum geometry has a semi-classical toroidal core.

Outgrowths contain most of the four-volume.

Outgrowths are fractal with spherical topology.

Abstract

We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with many outgrowths, which contain most of the four-volume and which have almost spherical topologies, but nevertheless are quite fractal.