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In this paper, we review the approach leading to cosmic polarization rotationobservation and present the current status with an outlook. In the study of therelations among equivalence principles, we found that long-rangepseudoscalar-photon interaction is allowed. Pseudoscalar-photon interactionwould induce a rotation of linear polarization of electromagnetic wavepropagating with cosmological/astrophysical distance. In 2002, DASIsuccessfully observed the polarization of the cosmological microwave backgroundradiation. In 2003, WMAP observed the correlation of polarization withtemperature anisotropy at more than 10 sigma in the cosmological microwavebackground. From this high polarization-temperature correlation in WMAPobservation, we put a limit of 0.1 rad on the rotation of linear polarizationof cosmological microwave background (CMB) propagation. Pseudoscalar-photoninteraction is proportional to the gradient of the pseudoscalar field. Fromphenomenological point of view, this gradient could be neutrino numberasymmetry current, other density current, or a constant vector. In thesesituations, Lorentz invariance or CPT may or may not effectively be violated.In this paper, we review and compile various results. Better accuracy in CMBpolarization observation is expected from PLANCK mission to be launched nextyear. A dedicated CMB polarization observer in the future would probe thisfundamental issue more deeply.

From Equivalence Principles to Cosmology: Cosmic Polarization Rotation, CMB Observation, Neutrino Number Asymmetry, Lorentz Invariance and CPT