Quantum Flatness in Two-Dimensional CDT Quantum Gravity

Abstract

Flatness -the absence of spacetime curvature -is a well-understood property of macroscopic, classical spacetimes in general relativity. The same cannot be said about the concepts of curvature and flatness in nonperturbative quantum gravity, where the microscopic structure of spacetime is not describable in terms of small fluctuations around a fixed background geometry. An interesting case are two-dimensional models of quantum gravity, which lack a classical limit and therefore are maximally "quantum". We investigate the recently introduced quantum Ricci curvature in CDT quantum gravity on a two-dimensional torus, whose quantum geometry could be expected to behave like a flat space on suitably coarsegrained scales. On the basis of Monte Carlo simulations we have performed, with system sizes of up to 600.000 building blocks, this does not seem to be the case. Instead, we find a scale-independent "quantum flatness", without an obvious classical analogue. As part of our study, we develop a criterion that allows us to distinguish between local and global, topological properties of the toroidal quantum system.

Emergent time, cosmological constant and boundary dimension at infinity in combinatorial quantum gravity

“…The negative curvature of the ground state was recently identified also using the above mentioned [24,25] Ollivier curvature approximation in 2D [34]. It was, however dismissed in favour of a new concept of "quantum flatness" because of the lack of a mechanism for the spontaneous emergence of a curvature scale.…”