Non-perturbative 3d Lorentzian Quantum Gravity

TL;DR

This paper presents a non-perturbative Lorentzian quantum gravity model in three dimensions, showing that it dynamically generates a semi-classical universe with promising properties for a quantum gravity theory.

Contribution

It introduces a discrete Lorentzian quantum gravity model and demonstrates its phase structure and emergence of extended geometries through computer simulations.

Findings

Existence of a phase with non-degenerate 3D space-times

Emergence of a semi-classical spherical universe

Scale invariance in the continuum limit

Abstract

We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to Euclidean signature. We investigate here the phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations. After fine-tuning the cosmological constant to its critical value, we find a whole range of the gravitational coupling constant $k_0$ for which the functional integral is dominated by non-degenerate three-dimensional space-times. We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a non-perturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semi-classical spherical universe. Measurements so far indicate that $k_0$ defines an overall scale in this extended phase, without affecting the physics of the continuum limit. These findings provide further evidence that discrete {\it Lorentzian} gravity is a promising candidate for a non-trivial theory of quantum gravity.