Structure of the cosmic microwave background

Mathematics – Logic

Scientific paper

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Astronomical Models, Cosmic Rays, Cosmology, Microwave Emission, Radiation Distribution, Relic Radiation, Temperature Profiles, Background Radiation, Extraterrestrial Radiation, Quadrupoles

Scientific paper

Temperature profiles of the cosmic microwave background generated by anisotropic and inhomogeneous cosmological models are used to define two distinct sky patterns for angular variations of the radiation. The Bianchi type I axisymmetric model and the homogeneous Kantowski-Sachs model, which yields a pure quadrupole temperature profile, are discussed for the case of nonisothermal microwave background temperatures. A Bianchi type V model is shown to describe a homogeneous, anisotropic universe where a quadrupole pattern will be concentrated in a small region of sky. A formulation is presented for the microwave temperature pattern, and it is noted that a large z value results in a pure quadrupole focused into a region of decreasing angular scale. Attention is also given to the evolution of small pressureless density inhomogeneities in a flat Friedmann universe and to the shear evolution. It is concluded that the discovery of a hot spot would provide substantial evidence for an open universe.

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