Quantum widening of CDT universe

TL;DR

This paper maps the effective description of the CDT universe onto a statistical physics model, revealing phase transitions and quantum corrections, and predicting potential new phases consistent with CDT simulations.

Contribution

It introduces a novel statistical physics model for the CDT universe's effective dynamics, reproducing observed phases and predicting additional phases based on the effective action.

Findings

Reproduces the shape of the quantum universe in CDT

Identifies the emergence of the de-Sitter universe as a condensation transition

Predicts two additional phases depending on model parameters

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.