Cosmic Clustering

TL;DR

This paper reveals that the late-time Hartle-Hawking wave function in de Sitter space exhibits an ultrametric, hierarchical structure similar to spin glass models, providing new insights into the organization of quantum states in cosmology.

Contribution

It establishes a novel connection between quantum cosmology and spin glass theory by demonstrating ultrametricity in the wave function of a scalar field in de Sitter space.

Findings

Ultrametric structure in the wave function encodes hierarchical organization.

Hierarchical organization reflects a branched diffusion process.

Mathematical analogy with spin glass models like Sherrington-Kirkpatrick.

Abstract

We show that the late time Hartle-Hawking wave function for a free massless scalar in a fixed de Sitter background encodes a sharp ultrametric structure for the standard Euclidean distance on the space of field configurations. This implies a hierarchical, tree-like organization of the state space, reflecting its genesis as a branched diffusion process. An equivalent mathematical structure organizes the state space of the Sherrington-Kirkpatrick model of a spin glass.