Where do all the supercurvature modes go?
J.D. Cohn, D.I. Kaiser
TL;DR
This paper investigates the behavior and mathematical representation of supercurvature modes in open universe models within de Sitter space, focusing on their expression in different coordinate slicings.
Contribution
It provides a new formulation of normalizable vacuum supercurvature modes for a massless scalar field in hyperbolic slicing of de Sitter space.
Findings
Supercurvature modes are present in the Bunch-Davies vacuum.
Normalizable supercurvature modes can be expressed in flat slicing basis.
The work clarifies the role of supercurvature modes in open universe models.
Abstract
In the hyperbolic slicing of de Sitter space appropriate for open universe models, a curvature scale is present and supercurvature fluctuations are possible. In some cases, the expansion of a scalar field in the Bunch-Davies vacuum includes supercurvature modes, as shown by Sasaki, Tanaka and Yamamoto. We express the normalizable vacuum supercurvature modes for a massless scalar field in terms of the basis modes for the spatially-flat slicing of de Sitter space.
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