**AAS Meeting #193 - Austin, Texas, January 1999**

*Session 39. Cosmology/Large Scale Structure*

Display, Thursday, January 7, 1999, 9:20am-6:30pm, Exhibits Hall 1
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## [39.02] CMB Polarization statistics as a probe of Scalar and Tensor perturbations

*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.

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