Causal Dynamical Triangulations without Preferred Foliation

TL;DR

This paper generalizes Causal Dynamical Triangulations (CDT) by removing the preferred foliation, demonstrating through numerical simulations in 2+1 dimensions that an extended de Sitter universe still emerges, indicating foliation is not essential.

Contribution

It introduces a foliation-independent version of CDT and shows it can still produce realistic large-scale spacetime geometries.

Findings

Reproduces de Sitter universe without preferred foliation

Foliation is not a necessary background structure in CDT

Supports broader applicability of causal triangulation methods

Abstract

We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories retain their causal properties, but do not have a preferred proper-time foliation. An extensive numerical study of the associated nonperturbative path integral in 2+1 dimensions shows that it can nevertheless reproduce the emergence of an extended de Sitter universe on large scales, a key feature of CDT quantum gravity. This suggests that the preferred foliation normally used in CDT is not a crucial (albeit convenient) part of its background structure.