Exploring torus universes in causal dynamical triangulations

T. G. Budd and R. Loll
Phys. Rev. D 88, 024015 – Published 9 July 2013

Abstract

Motivated by the search for new observables in nonperturbative quantum gravity, we consider causal dynamical triangulations in 2+1 dimensions with the spatial topology of a torus. This system is of particular interest, because one can study not only the global scale factor, but also global shape variables in the presence of arbitrary quantum fluctuations of the geometry. Our initial investigation focuses on the dynamics of the scale factor and uncovers a qualitatively new behavior, which leads us to investigate a novel type of boundary conditions for the path integral. Comparing large-scale features of the emergent quantum geometry in numerical simulations with a classical minisuperspace formulation, we find partial agreement. By measuring the correlation matrix of volume fluctuations we succeed in reconstructing the effective action for the scale factor directly from the simulation data. Apart from setting the stage for the analysis of shape dynamics on the torus, the new setup highlights the role of nontrivial boundaries and topology.

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  • Received 3 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.024015

© 2013 American Physical Society

Authors & Affiliations

T. G. Budd1,* and R. Loll2,3,†,‡

  • 1The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
  • 2Radboud University Nijmegen, Institute for Mathematics, Astrophysics, and Particle Physics, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands
  • 3Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada

  • *budd@nbi.dk
  • r.loll@science.ru.nl
  • rloll@perimeterinstitute.ca

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Vol. 88, Iss. 2 — 15 July 2013

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