On Generalised Statistical Equilibrium and Discrete Quantum Gravity

TL;DR

This paper develops a generalized statistical equilibrium framework for background independent quantum gravity systems, using Gibbs states and many-body techniques, and applies it to derive cosmological dynamics with a bounce and accelerated expansion.

Contribution

It introduces a novel approach to defining statistical equilibrium in background independent quantum gravity, utilizing generalized Gibbs states and entanglement-based representations.

Findings

Derived classical Friedmann equations from quantum gravity states

Constructed concrete examples of quantum gravitational Gibbs states

Demonstrated early universe bounce and accelerated expansion

Abstract

Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime should emerge from the collective physics of the underlying quantum gravitational degrees of freedom. However, defining statistical equilibrium in a background independent system is a challenging open issue, mainly due to the absence of absolute notions of time and energy. This is especially so in non-perturbative quantum gravity frameworks that are devoid of usual space and time structures. In this thesis, we investigate aspects of a generalisation of statistical equilibrium, specifically Gibbs states, suitable for background independent systems. We emphasise on an information theoretic characterisation based on the maximum entropy principle. Subsequently, we explore the resultant generalised Gibbs states in a discrete quantum gravitational system composed of many candidate quanta of geometry, utilising their field theoretic formulation of group field theory and various many-body techniques. We construct several concrete examples of quantum gravitational generalised Gibbs states. We further develop inequivalent thermal representations based on entangled, two-mode squeezed, thermofield double vacua, induced by a class of generalised Gibbs states. In these representations, we define a class of thermal condensates which encode statistical fluctuations in a given observable, e.g. volume of the quantum geometry. We apply these states in the condensate cosmology programme of group field theory to study a relational effective cosmological dynamics extracted from a class of free models, for homogeneous and isotropic spacetimes. We find the correct classical limit of Friedmann equations at late times, with a bounce and accelerated expansion at early times.