On memory in exponentially expanding spaces

Understand

We examine the degree to which fluctuating dynamics on exponentially expanding spaces remember initial conditions.

• In de Sitter space, the global late-time configuration of a free scalar field always contains information about early fluctuations.
• By contrast, fluctuations near the boundary of Euclidean Anti-de Sitter may or may not remember conditions in the center, with a transition at \Delta=d/2.
• We connect these results to literature about statistical mechanics on trees and make contact with the observation by Anninos and Denef that the configuration space of a massless dS field exhibits ultrametricity.