Cosmic microwave anisotropies from topological defects in an open universe

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Abstract
We present a general formalism for computing cosmic background radiation (CBR) and density fluctuations in open models with stiff sources. We decompose both the metric fluctuations and the fluctuations in the stress-energy tensor into scalar, vector, and tensor modes. We find analytic Green’s functions for the linearized Einstein equations in the presence of stiff sources and use this formalism to estimate the amplitude and harmonic spectrum of microwave background fluctuations produced by topological defects in an open universe. Unlike inflationary models that predict a flat universe and a spectrum of CBR fluctuations that are enhanced at large angular scales, defect models predict that CBR fluctuations are suppressed on angular scales larger than that subtended by the curvature scale. In an Ω=0.2–0.4 universe, these models, when normalized to the amplitude of CBR fluctuations observed by COBE, require a moderate bias factor, 2–3, to be compatible with the observed fluctuations in galaxy counts. In these models, accurate predictions can be made which are testable through CBR experiments in the near future. A CBR measurement of Ω would then be possible, up to the limit imposed by cosmic variance. We discuss some of the philosophical implications of an open model and propose a solution to the flatness problem.
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