Measuring the Homogeneity (or Otherwise) of the Quantum Universe
arXiv:2302.10256 · doi:10.1103/PhysRevD.107.086013
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.
arXiv comment30 pages, 7 figures
References in corpus (31)
- Spectral Dimension of the Universe
- Emergence of a 4D World from Causal Quantum Gravity
- Reconstructing the Universe
- Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
- Nonperturbative Quantum Gravity
- Quantum Gravity from Causal Dynamical Triangulations: A Review
- Dynamically Triangulating Lorentzian Quantum Gravity
- Is the Observable Universe Consistent with the Cosmological Principle?
- Planckian Birth of the Quantum de Sitter Universe
- The Nonperturbative Quantum de Sitter Universe
- Diffeomorphism-invariant observables and their nonlocal algebra
- Scaling in four dimensional quantum gravity
- Inhomogeneity effects in Cosmology
- A new perspective on matter coupling in 2d quantum gravity
- Renormalization Group Flow in CDT
- The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
- On the spectral dimension of causal triangulations
- Quantum geometry of 2d gravity coupled to unitary matter
- On the relation between Euclidean and Lorentzian 2D quantum gravity
- Singular Vertices and the Triangulation Space of the D-sphere
- Introducing Quantum Ricci Curvature
- Quantizing quantum Ricci curvature
- Inhomogeneous cosmology and backreaction: Current status and future prospects
- Backreaction in Cosmology
- How round is the quantum de Sitter universe?
- Propagators for gauge-invariant observables in cosmology
- Locally Causal Dynamical Triangulations in Two Dimensions
- Scale-dependent homogeneity measures for causal dynamical triangulations
- Quantum Flatness in Two-Dimensional CDT Quantum Gravity
- Coarse graining dynamical triangulations: a new scheme
- Approximate Killing symmetries in non-perturbative quantum gravity