Homothetic expansion of polyhedra in the two-vertex model: emergence of FLRW

TL;DR

This paper explores how polyhedra in a simplified quantum gravity model undergo homothetic expansion, revealing a connection to classical cosmological models like FLRW, through the analysis of twisted geometries and phase space structures.

Contribution

It introduces a new framework for understanding the classical phase space of twisted geometries in the two-vertex model and demonstrates homothetic expansion consistent with FLRW cosmology.

Findings

Polyhedra exhibit homothetic expansion under evolution.

The model strengthens the link between quantum geometry and classical FLRW cosmology.

Constructed phase space bases encode the entire classical twisted geometry.

Abstract

The cosmological behavior associated to a U(N)-symmetry reduced sector of the loop-quantum-gravity truncation known as the two-vertex model is further explored in this work. We construct convenient frame bases that encode the whole classical phase space of the twisted geometry associated to the graph. We show that the polyhedra of the twisted geometry suffer under evolution an homothetic expansion, which strengthens the correspondence to the Robertson-Walker geometry.