On memory in exponentially expanding spaces

TL;DR

This paper explores how initial conditions influence the late-time configurations of fields in exponentially expanding spaces like de Sitter and Anti-de Sitter, revealing conditions under which memory persists or fades.

Contribution

It provides a comparative analysis of memory effects in de Sitter and Anti-de Sitter spaces, extending previous work to massive fields and connecting to statistical mechanics on trees.

Findings

Global de Sitter configurations retain early fluctuations.

Boundary Anti-de Sitter memory depends on d7d/2 transition.

Massive fields show persistent ultrametricity for d7d/4.

Abstract

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. We extend their analysis to massive fields, finding that preference for isosceles triangles persists as long as \Delta_- < d/4.