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D.I. Novikov (Univ. of Kansas)
The distribution of the Cosmic Microwave Background (CMB) polarization in the sky is determined by the hypothesis of Gaussianity of the primordial perturbations. This hypotheses is well motivated by the inflationary cosmology. Statistical properties of the CMB polarization field depend also on the nature of the initial perturbations - scalar or tensor (gravitational waves).
This paper contains the theoretical predictions of the statistical properties of the CMB polarization field for two different types of the primordial Gaussian inhomogeneities. I pay the special attention to the following two problems. First, the classification and statistics of the singular points of the polarization field where polarization is equal to zero. This statistics is invariant with respect to the type of perturbations and can be considered only as a test on Gaussianity. Second, Minkowski functionals for the CMB polarization field. These functionals are determined by the covariance matrix of second derivatives of Stokes parameters. This matrix is different for scalar and tensor mode. Therefore, Minkowski functionals for CMB polarization field can be considered as a probe of scalar perturbations and gravitational waves. All results are analytical.
This approach is also very sensitive to the presence of the non-Gaussian (non-cosmological noise) and can be used as a detector of a noise in the observational data for future experiments - MAP and Planck.