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

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.

16 pages, 16 figures

References in corpus (5)

• Quantum Gravity at a Lifshitz Point
• Nonperturbative Quantum Gravity
• The Nonperturbative Quantum de Sitter Universe
• Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity
• The effective action in 4-dim CDT. The transfer matrix approach

Cited by in corpus (5)

• Cosmic voids and filaments from quantum gravity
• Scalar fields in Causal Dynamical Triangulations
• Matter-driven change of spacetime topology
• Generalised spectral dimensions in non-perturbative quantum gravity
• CDT Quantum Toroidal Spacetimes: An Overview