Normalization of modes in an open universe

Abstract

We discuss the appropriate normalization of modes required to generate a homogeneous random field in an open Friedmann-Robertson-Walker universe. We consider scalar random fields and certain tensor random fields that can be obtained by covariantly differentiating a scalar. Modes of interest fall into three categories: the familiar sub-curvature modes, the more recently discussed super-curvature modes, and a set of discrete modes with positive eigenvalues which can be used to generate homogeneous tensor random fields even though the underlying scalar field is not homogeneous. A particular example of the last case which has been discussed in the literature is the bubble wall fluctuation in open inflationary universes.

8 pages LaTeX file (using RevTeX). Some restructuring of the arguments and additional material added; no changes to existing formulae or to the principal results

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• Self Excitation of the Tunneling Scalar Field in False Vacuum Decay
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• Cosmological magnetic field survival
• Open Hybrid Inflation
• Open inflation models and gravitational wave anisotropies in the CMB
• Complete power spectrum for an induced gravity open inflation model
• Microwave background anisotropies in quasiopen inflation
• Fluctuations in the Hawking Turok model
• Variational dynamics in open spacetimes