On memory in exponentially expanding spaces

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 Δ=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 Δ_- < d/4.

30 pages plus appendices, with 6 figures. Journal version (JHEP). Presentation clarified, sections rearranged, and references added

References in corpus (10)

• The IR stability of de Sitter: Loop corrections to scalar propagators
• De Sitter Musings
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• A Holographic Framework for Eternal Inflation
• Eternal Symmetree
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• Higher Spin de Sitter Holography from Functional Determinants
• Amplitudes meet Cosmology: A (Scalar) Primer
• The Geometry of Cosmological Correlators
• Higher Spin de Sitter Hilbert Space
• FRW cosmologies and hyperscaling-violating geometries: higher curvature corrections, ultrametricity, Q-space/QFT duality, and a little string theory
• Late-time Structure of the Bunch-Davies FRW Wavefunction
• Noisy Quantum Trees: Infinite Protection Without Correction