0419-Stokes parameter

WHY

What is polarization field and what is the right way to characterize it???

What do they mean: "Polarization, which is described by a second-rank tensor"?

WHY CMB polarization fluctuations are characteristically at a part in $10^6$, an order of magnitude below the temperature fluctuations?

a net polarization arises from Compton scattering only when the incident radiation field possesses a nonzero quadrupole moment @16,13#, but only monopole and dipole fluctuations are possible as long as the photons in the Universe remain tightly coupled to the charged electrons. Polarization is only generated very near the surface of last scattering as the photons begin to decouple from the electrons and generate a quadrupole moment through free streaming. Since by this time most of the electrons have recombined into neutral hydrogen, the number of scatterers available to produce polarization is reduced.

Stokes parameter [ CMB ]

The Stokes parameters conventionally used to describe polarization are not invariant under rotations of the coordinate system used to describe them, unlike temperature fluctuations, but rather transform as a second-rank tensor.

Why no V parameter?

The Compton scattering process which thermalizes the CMB and generates polarization cannot produce any net circular polarization; thus we expect V50 for the microwave background and do not consider the V Stokes parameter further. [EOF]

In linear theory, scalar perturbations can produce only G-type polarization and not C-type polarization. On the other hand, tensor or vector metric perturbations will produce a mixture of both types. Heuristically, this is because scalar perturbations have no handedness so they cannot produce any ‘‘curl,’’ whereas vector and tensor perturbations do have a handedness and therefore can.

ENGLISH WORD I

• Incidentally: by the way