2024/03/04 by Bianca Dittrich, Ted Jacobson, José Padua-Argüelles · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Geometric Analysis and Curvature Flows #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.110.046006
arxiv published 2024/03/04 · openalex publication_date 2024/08/06 · arxiv updated 2024/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The dimension of the Hilbert space of a quantum gravitational system can be written formally as a path integral partition function over Lorentzian metrics. We implement this in a (2+1)-dimensional simplicial minisuperspace model in which the system is a spatial topological disc, and recover by contour deformation through a Euclidean saddle the entropy of the de Sitter static patch, up to discretization artifacts. The model illustrates the importance of integration over both positive and negative lapse to enforce the gravitational constraints, and of restriction to complex metrics for which the fluctuation integrals would converge. Although a strictly Lorentzian path integral is oscillatory, an exponentially large partition function results from unavoidable imaginary contributions to the action. These arise from analytic continuation of the simplicial (Regge) action for configurations with codimension-2 simplices where the metric fails to be Lorentzian. In particular, the dominant contribution comes from configurations with contractible closed timelike curves that encircle the boundary of the disc, in close correspondence with recent continuum results.