Cosmological birefringence induced by neutrino current

We review our recent work on the cosmological birefringence. We propose a new type of effective interactions in terms of the $CPT$-even dimension-six Chern-Simons-like term to generate the cosmological birefringence. We use the neutrino number asymmetry to induce a non-zero rotation polarization angle in the data of the cosmic microwave background radiation polarization.