Where do all the Supercurvature Modes Go

(1) Departments of Physics and Astronomy, University of IllinoisUrbana-Champaign, IL 61801jdc@uiuc.edu(2) Department of Physics, Harvard UniversityCambridge, MA 02138dkaiser@fas.harvard.edu(March 1998)In the hyperbolic slicing of de Sitter space appropriate for open universe models, a curvaturescale is present and supercurvature fluctuations are possible. In some cases, the expansion of a scalarfield in the Bunch-Davies vacuum includes supercurvature modes, as shown by Sasaki, Tanaka andYamamoto. We express the normalizable vacuum supercurvature modes for a massless scalar fieldin terms of the basis modes for the spatially-flat slicing of de Sitter space.Preprint UIUC-98/2; HUTP-98/A010; gr-qc/9803073I. INTRODUCTION