Causal Dynamical Triangulations: New Lattice Theory of Quantum Gravity

TL;DR

Causal Dynamical Triangulations (CDT) offers a nonperturbative lattice approach to quantum gravity, demonstrating emergent spacetime properties and potential ultraviolet fixed points through Monte Carlo simulations.

Contribution

This paper introduces CDT as a lattice framework incorporating causality and dynamical spacetime, with evidence of a classical limit and quantum fluctuations.

Findings

Emergence of a quantum universe resembling de Sitter space

Spectral dimension reduces to near 2 at short scales

Indications of an ultraviolet fixed point in the theory

Abstract

Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of nongravitational quantum fields, CDT provides a blueprint for lattice quantum gravity, where - crucially - the dynamical, curved and causal nature of spacetime is built into the structure of the lattices from the outset. The regularized path integral involves a sum over triangulated spacetimes, each assembled from flat, Minkowskian building blocks. The degrees of freedom of general relativity are encoded in a coordinate-free manner in the neighbourhood relations of the building blocks and the length of their edges, which also serves as a short-distance cutoff. A well-defined Wick rotation makes this path integral amenable to Monte Carlo simulations. Despite the absence of an a priori preferred background geometry, numerical experiments have revealed the dynamical emergence of a quantum universe near the Planck scale. Its global properties are compatible with those of a de Sitter space, providing strong evidence for a well-defined classical limit. At the same time, large quantum fluctuations lead to unexpected properties on short scales, most prominently, a spectral dimension near 2, replacing the classical value of 4. Computer simulations indicate the presence of an ultraviolet fixed point under renormalization, opening the door to a nontrivial continuum theory. Efforts are under way to construct observables that can elucidate the nonperturbative quantum origins of early-universe cosmology.