Exploring Torus Universes in Causal Dynamical Triangulations

Abstract

Motivated by the search for new observables in nonperturbative quantum gravity, we consider Causal Dynamical Triangulations (CDT) in 2+1 dimensions with the spatial topology of a torus. This system is of particular interest, because one can study not only the global scale factor, but also global shape variables in the presence of arbitrary quantum fluctuations of the geometry. Our initial investigation focusses on the dynamics of the scale factor and uncovers a qualitatively new behaviour, which leads us to investigate a novel type of boundary conditions for the path integral. Comparing large-scale features of the emergent quantum geometry in numerical simulations with a classical minisuperspace formulation, we find partial agreement. By measuring the correlation matrix of volume fluctuations we succeed in reconstructing the effective action for the scale factor directly from the simulation data. Apart from setting the stage for the analysis of shape dynamics on the torus, the new set-up highlights the role of nontrivial boundaries and topology.

30 pages, 12 figures

References in corpus (10)

• Nonperturbative Quantum Gravity
• The Nonperturbative Quantum de Sitter Universe
• Second- and First-Order Phase Transitions in CDT
• Quantum Gravity via Causal Dynamical Triangulations
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• Causal Dynamical Triangulations without Preferred Foliation
• Causal Dynamical Triangulations and the Quest for Quantum Gravity
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• The emergence of background geometry from quantum fluctuations
• CDT---an Entropic Theory of Quantum Gravity

Cited by in corpus (9)

• Quantum Gravity via Causal Dynamical Triangulations
• De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• The phase structure and effective action of 3D CDT at higher spatial genus
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Minisuperspace results for causal dynamical triangulations
• Making the case for causal dynamical triangulations
• Landau Theory of Causal Dynamical Triangulations