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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.

### Author and article information

###### Journal
31 January 1995
astro-ph/9501113
10.1111/j.1749-6632.1995.tb17639.x