Quantum gravity on polygons and R×Zn FLRW model *

Abstract

Abstract We fully solve the quantum geometry of Z n as a polygon graph with arbitrary metric square-lengths on the edges, finding a ∗-preserving quantum Levi-Civita connection which is unique for n ≠ 4. As a first application, we numerically compute correlation functions for Euclideanised quantum gravity on Z n for small n. We then study an FLRW model on R × Z n , finding the same expansion rate as for the classical flat FLRW model in 1 + 2 dimensions. We also look at particle creation on R × Z n and find an additional m = 0 adiabatic no particle creation expansion as well as the particle creation spectrum for a smoothed step expansion.