  Effective pseudoscalar-photon interaction(s) would induce a rotation of
linear polarization of electromagnetic wave propagating with cosmological
distance in various cosmological models. Pseudoscalar-photon interaction is
proportional to the gradient of the pseudoscalar field. From phenomenological
point of view, this gradient could be neutrino number asymmetry, other density
current, or a constant vector. In these situations, Lorentz invariance or CPT
may effectively be violated. CMB polarization observations are superb tests of
these models and have the potential to discover new fundamental physics. In
this paper, we review the constraints on pseudoscalar-photon interaction from
CMB polarization observation.

General Relativity and Quantum Cosmology