Cosmic birefringence fluctuations and cosmic microwave background B-mode polarization

Recently, BICEP2 measurements of the cosmic microwave background (CMB) B  -mode polarization has indicated the presence of primordial gravitational waves at degree angular scales, inferring the tensor-to-scalar ratio of r=0.2r=0.2 and a running scalar spectral index, provided that dust contamination is low. In this Letter, we show that the existence of the fluctuations of cosmological birefringence can give rise to CMB B  -mode polarization that fits BICEP2 data with r<0.11r<0.11 and no running of the scalar spectral index. When dust contribution is taken into account, we derive an upper limit on the cosmological birefringence, Aβ2<0.0075Aβ2<0.0075, where A is the amplitude of birefringence fluctuations that couple to electromagnetism with a coupling strength β.