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arXiv · 1210.5238

On memory in exponentially expanding spaces

Daniel A. Roberts·Douglas Stanford
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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.

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Daniel A. Roberts, Douglas Stanford. 2012-10-18. On memory in exponentially expanding spaces. https://doi.org/10.1007/jhep06(2013)042

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