TL;DR
This paper applies spin glass theory to analyze the phase space of a scalar field in a 1+1 dimensional de Sitter universe, revealing a Gumbel distribution for overlaps and a product form for triple overlaps.
Contribution
It introduces a novel application of spin glass methods to cosmological scalar fields, deriving explicit overlap distributions in a simplified de Sitter model.
Findings
Overlap distribution follows a Gumbel distribution after rescaling.
Triple overlap characteristic function is a product of two Gumbel factors.
Provides new insights into the structure of scalar fields in inflating universes.
Abstract
In this note we employ methods borrowed from spin glass theory to study the phase space structure of fields in an inflating universe. In particular, we compute the overlap distribution of a suitably coarse-grained, massless scalar on a 1+1 dimensional (hence baby) de Sitter background, and find that (after an appropriate shift and rescaling) it is given by a Gumbel distribution. We also calculate the triple overlap distribution of this system, whose characteristic function turns out to be a product of two Gumbel factors.
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