Cosmological states in loop quantum gravity on homogeneous graphs

TL;DR

This paper introduces homogeneous and isotropic states in loop quantum gravity using Bell-network states on specific graphs, providing new cosmological models with automorphism-invariant local geometry and entanglement entropy measures.

Contribution

It constructs explicit homogeneous and isotropic states in loop quantum gravity and analyzes their local geometry and entanglement properties.

Findings

States exhibit automorphism-invariant local geometry.

Density matrix and entanglement entropy are computed for these states.

Framework allows superpositions of different graphs in cosmological models.

Abstract

We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states provide new representations of cosmological spaces that can be explored for the formulation of cosmological models in the context of loop quantum gravity. We show that their local geometry is described in an automorphism-invariant manner by one-node observables analogous to the one-body observables used in many-body quantum mechanics, and compute the density matrix representing the restriction of global states to the algebra of one-node observables. The von Neumann entropy of this density matrix provides a notion of entanglement entropy of a local region which respects automorphism-invariance and can be applied to states involving superpositions of distinct graphs.