  CMB (Cosmic Microwave Background) polarization observations test many aspects
of cosmological models. Effective pseudoscalar-photon interaction(s) would
induce a rotation of linear polarization of electromagnetic wave propagating
with cosmological distance in various cosmological models. CMB polarization
observations are superb tests of these models and have the potential to
discover new fundamental physics. 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. In this paper, we review these results and
anticipate what more precise observations can tell us about fundamental
physics, inflation, etc. Better accuracy in CMB polarization observation is
expected from PLANCK mission to be launched this year. Dedicated CMB
polarization observers like B-Pol mission, CMBpol mission and LiteBIRD mission
would probe this fundamental issue more deeply in the future. With these
sensitivities, cosmic polarization rotations from effective pseudoscalar-photon
interaction, Faraday polarization rotations from primordial and large-scale
magnetic field, and tensor modes effects would have chances to be detected and
distinguished. The subtracted tensor-mode effects are likely due to primordial
gravitational waves. We discuss the direct detectability of these primordial
gravitational waves using space GW detectors.
