Measuring the Homogeneity (or Otherwise) of the Quantum Universe

TL;DR

This paper introduces new quantum observables to quantitatively assess the homogeneity of a quantum universe's geometric properties across scales, aiding comparisons between quantum gravity models and early universe assumptions.

Contribution

It proposes a background-independent, purely geometric method to measure quantum homogeneity, demonstrated through application to 2D Lorentzian quantum gravity.

Findings

Evidence of quantum inhomogeneity in 2D Lorentzian quantum gravity

New tools for comparing quantum gravity results with cosmological models

Quantitative measures of geometric homogeneity at different scales

Abstract

There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we introduce new quantum observables that allow us to measure the absolute and relative homogeneity of geometric properties of a nonperturbative quantum universe, as function of a chosen averaging scale. This opens a new way to compare results obtained in full quantum gravity to descriptions of the early universe that assume homogeneity and isotropy at the outset. Our construction is purely geometric and does not depend on a background metric. We illustrate the viability of the quantum homogeneity measures by a nontrivial application to two-dimensional Lorentzian quantum gravity formulated in terms of a path integral over Causal Dynamical Triangulations, and find some evidence of quantum inhomogeneity.