Cosmic Clustering
  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. 
Dionysios Anninos and Frederik Denef
hep-th gr-qc