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THE GRISHCHUK-ZELDOVICH EFFECT IN THE OPEN UNIVERSE

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      Abstract

      When considering perturbations in an open universe, cosmologists retain only sub-curvature modes (defined as eigenfunctions of the Laplacian whose eigenvalue is less than \(-1\) in units of the curvature scale, in contrast with the super-curvature modes whose eigenvalue is between \(-1\) and \(0\)). Mathematicians have known for almost half a century that all modes must be included to generate the most general {\em homogeneous Gaussian random field}, despite the fact that any square integrable {\em function} can be generated using only the sub-curvature modes. The former mathematical object, not the latter, is the relevant one for physical applications. This article summarizes recent work with A. Woszczyna. The mathematics is briefly explained in a language accessible to physicists. Then the effect on the cmb of any super-curvature contribution is considered, which generalizes to \(\Omega_0<1\) the analysis given by Grishchuk and Zeldovich in 1978.

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      Journal
      31 January 1995
      astro-ph/9501113
      10.1111/j.1749-6632.1995.tb17639.x
      Custom metadata
      Annals N.Y.Acad.Sci.759:701,1995
      5 pages latex; Munich conference report summarizing astro-ph/9501044 with an improved discussion of the physical significance.
      astro-ph gr-qc hep-ph

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