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The B-mode polarization of the cosmic microwave background (CMB) radiation isan excellent information channel for the detection of relic gravitationalwaves. However, the detection is contaminated by the B-mode polarizationgenerated by some other effects. In this paper, we discuss the contaminationscaused by the cosmological birefringence, which converts the CMB E-mode to theB-mode, and forms the effective noise for the detection of gravitational waves.We find that this contamination is significant, if the rotation angle is large.However, this kind of B-mode can be properly de-rotated, and the effectivenoises can be greatly reduced. We find that, comparing with the contaminationscaused by cosmic weak lensing, the residual polarization generated by thecosmological birefringence is negligible for the detection of relicgravitational waves in the CMB.

Detecting relic gravitational waves in the CMB: The contamination caused by the cosmological birefringence