0 On the Local Separation of E and B Polarization Patterns in the CMBR

This work examines the small-scale E and B patterns of the Cosmic Microwave Background Radiation (CMBR) polarization anisotropy. Particularly, we address the topologi-cal natures and spatial symmetries of the E and B modes, and how one may make use of the local measurements of Stokes parameters to separate these two modes. We point out that the separation of these two modes in a local map of Stokes parameters is in fact an ill-posed problem due to the unknown boundary conditions of these modes at the edges of the map. A valid strategy for local separation of them can be through the construction of a [(charge)+i (current)] 2 map of polarization, where i = √ −1. In the standard CMBR paradigm, only E modes are detectable and the real part of such a map has patterns which contain point caustics at locations of null polarization, and the imaginary part vanishes. However, if detectable B modes should exist, the imaginary part of this map will also contain patterns with point caustics. The spatial distribution of these point caustics ought to reflect the statistical properties of the polarization field.