Effective de Sitter space, quantum behaviour and large-scale spectral dimension (3+1)

TL;DR

This paper proposes that our universe's de Sitter space is an effective emergent phenomenon from a fundamental quantum gravity state modeled as a graph with negative curvature, leading to emergent relativistic and quantum behaviors.

Contribution

It introduces a model where de Sitter space emerges from a fundamental graph-based quantum gravity ground state with negative curvature, explaining large-scale spectral dimension and quantum behavior.

Findings

Large-scale spectral dimension is (3+1) regardless of microscopic topology.

Negative curvature induces emergent relativistic time and ballistic motion.

Quantum behavior arises as a sub-leading component of Brownian motion.

Abstract

De Sitter space-time, essentially our own universe, is plagued by problems at the quantum level. Here we propose that Lorentzian de Sitter space-time is not fundamental but constitutes only an effective description of a more fundamental quantum gravity ground state. This cosmological ground state is a graph, appearing on large scales as a Riemannian manifold of constant negative curvature. We model the behaviour of matter near this equilibrium state as Brownian motion in the effective thermal environment of graph fluctuations, driven by a universal time parameter. We show how negative curvature dynamically induces the asymptotic emergence of relativistic coordinate time and of leading ballistic motion governed by the isometry group of an ``effective Lorentzian manifold" of opposite, positive curvature, i.e. de Sitter space-time: free fall in positive curvature is asymptotically equivalent to the leading behaviour of Brownian motion in negative curvature. The local limit theorem for negative curvature implies that the large-scale spectral dimension of this ``effective de Sitter space-time" is (3+1) independently of its microscopic topological dimension. In the effective description, the sub-leading component of asymptotic Brownian motion becomes Schr\"odinger quantum behavior on a 3D Euclidean manifold.