Quantum widening of CDT universe

Abstract

The physical phase of Causal Dynamical Triangulations (CDT) is known to be described by an effective, one-dimensional action in which three-volumes of the underlying foliation of the full CDT play a role of the sole degrees of freedom. Here we map this effective description onto a statistical-physics model of particles distributed on 1d lattice, with site occupation numbers corresponding to the three-volumes. We identify the emergence of the quantum de-Sitter universe observed in CDT with the condensation transition known from similar statistical models. Our model correctly reproduces the shape of the quantum universe and allows us to analytically determine quantum corrections to the size of the universe. We also investigate the phase structure of the model and show that it reproduces all three phases observed in computer simulations of CDT. In addition, we predict that two other phases may exists, depending on the exact form of the discretised effective action and boundary conditions. We calculate various quantities such as the distribution of three-volumes in our model and discuss how they can be compared with CDT.

19 pages, 13 figures

References in corpus (10)

• Quantum Gravity at a Lifshitz Point
• Nonperturbative Quantum Gravity
• The Nonperturbative Quantum de Sitter Universe
• The Semiclassical Limit of Causal Dynamical Triangulations
• Interaction driven real-space condensation
• Condensation and Extreme Value Statistics
• Condensation in zero-range processes on inhomogeneous networks
• Imposing causality on a matrix model
• Mass condensation in one dimension with pair-factorized steady states
• CDT as a scaling limit of matrix models

Cited by in corpus (7)

• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• Four-dimensional CDT with toroidal topology
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• Rényi Entropy of Zeta-Urns
• On Random Allocation Models in the Thermodynamic Limit
• Landau Theory of Causal Dynamical Triangulations