Question

Thomson scattering on the elections does not produce any circular polarization?

Answer 1

Yes, it is a consequence of the formulation of the Stokes parameters of the outgoing beam of a monochromatic unpolarized incident plane wave and can be generalised.

By symmetry, Thomson scattering can generate no circular polarization, so V = 0 always and will not be considered further.

Introduction to microwave background polarization chap 3 , Polarization from thomson scattering

Answer 2

This occurs because both V and I redshift as and hence the circular polarization fraction is unaffected by the expansion of the universe. On the other hand, with scatterings included, Thomson scattering exponentially diminishes circular polarization