Draft:Polarization E and B modes

Polarization patterns observed in sky can be separated into two components - Electric (E) and Magnetic (B).

The polarization patterns are due to Thomson scattering of photons off free electrons in the surface of last scattering.

Plane waves fluctuations (like density or scalar perturbations in the early universe) produce polarization patterns of a particular type, known as E mode. This polarization pattern is highly symmetrical with the observed orientation being independent of observation location while the observed magnitude is independent of longitude (for a fixed latitude of observation).

Gravitational wave can cause an anisotropic stretching of space, and this asymmetry causes a "handedness" to the pattern of polarization. Changing the viewing location, changes the observed orientation and magnitude of polarization (the pattern across all latitudes and longitudes becomes asymmetric). This polarization pattern is known as B mode.

There are two directions in a polarization pattern - its orientation and its amplitude. If the polarization orientation is parallel or perpendicular to its amplitude direction, it is called an E-mode polarization. If it is crossed at 45 degree angles, it is called a B-mode polarization.

Plane wave (density perturbations) just generate parallel polarization and so generate only E-mode polarization. Gravitational waves generate both and so have a component of B-mode polarization also.

B-modes retain their special nature that they can possess a handedness that distinguishes left from right. If reflected across a line going through the center the E-patterns are unchanged, while the positive and negative B-patterns get interchanged.