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Classification of singular points in the polarization field of the cosmic microwave background and eigenvectors of the Stokes matrix

A. D. DolgovInstitute of Theoretical and Experimental Physics, 117259, Moscow, RussiaA. G. DoroshkevichTheoretical Astrophysics Center, DK-2100, Copenhagen, DenmarkD. I. NovikovAstro-Space Center of Lebedev Physical Institute, Russian Academy of Sciences, 117924, Moscow, RussiaI. D. NovikovAstro-Space Center of Lebedev Physical Institute, Russian Academy of Sciences, 117924, Moscow, Russia
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An analysis is made of the singularities of the polarization field of the cosmic microwave background, where the polarization is equal to zero. It is found that the classification of the singular points differs from the usual three types known in ordinary differential equations. The new statistical properties of the polarization field are discussed, and new methods to detect the presence of primordial tensor perturbations are indicated.

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