Network gravity

John Lombard
Phys. Rev. D 95, 024001 – Published 3 January 2017

Abstract

We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with Forman weighted combinatorial curvatures and simplicial volumes relying on a decomposition of an abstract simplicial complex into realized embeddings of proper skeletons, we demonstrate properties such as a minimal volume-scale cutoff, the necessity of a term playing the role of a positive definite cosmological constant as a regulator for nondegenerate geometries, and naturally emergent simplicial structures from Metropolis network evolution simulations with no restrictions on attachment rules or regular building blocks. We see emergent properties which echo results from both the spinfoam formalism and causal dynamical triangulations in quantum gravity, and provide analytical and numerical results to support the analogy. We conclude with a summary of open questions and intent for future work in developing the program.

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  • Received 7 July 2016

DOI:https://doi.org/10.1103/PhysRevD.95.024001

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsNetworksStatistical Physics & ThermodynamicsInterdisciplinary PhysicsGeneral Physics

Authors & Affiliations

John Lombard*

  • University of Washington, Seattle, Washington 98195, USA

  • *jml448@uw.edu

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Issue

Vol. 95, Iss. 2 — 15 January 2017

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