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Published August 18, 2017 | Published + Supplemental Material
Journal Article Open

Navigability of Random Geometric Graphs in the Universe and Other Spacetimes

Abstract

Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.

Additional Information

© 2017 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Received: 21 March 2017; Accepted: 19 July 2017; Published online: 18 August 2017. We thank Alexander Vilenkin, Jaume Garriga, Ken Olum, Jiří Podolský, David Rideout, and Michel Buck for useful discussions. This work was supported by NSF grants Nos CNS-1442999 and CCF-1212778; and by ARO grant No. W911NF-16-1-0391. Author Contributions: D.K. and K.Z. designed research; W.C. and K.Z. performed research; W.C. and D.K. wrote the manuscript; all authors discussed the results and reviewed the manuscript. The authors declare that they have no competing interests.

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Created:
August 19, 2023
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October 17, 2023