Spacetime as a Complex Network and the Cosmological Constant Problem

Abstract

We propose a promising model of discrete spacetime based on nonassociative geometry and complex networks. Our approach treats space as a simplicial 3-complex (or complex network), built from “atoms” of spacetime and entangled states forming n-dimensional simplices (n=1,2,3). At large scales, a highly connected network is a coarse, discrete representation of a smooth spacetime. We show that, for high temperatures, the network describes disconnected discrete space. At the Planck temperature, the system experiences phase transition, and for low temperatures, the space becomes a triangulated discrete space. We show that the cosmological constant depends on the Universe’s topology. The “foamy” structure, analogous to Wheeler’s “spacetime foam”, significantly contributes to the effective cosmological constant, which is determined by the Euler characteristic of the Universe.