Abstract
We examine the effects of the axion coupling to $R\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{R}$ on the evolution of cosmic structures. It is shown that the evolutions of the scalar- and vector-type perturbations are not affected by this axion coupling. However, the axion coupling causes an asymmetric evolution of the two polarization states of the tensor-type perturbation, which may lead to a sizable polarization asymmetry in the cosmological gravitational wave if inflation involves a period in which the axion coupling is important. The polarization asymmetry produced during inflation is conserved over the subsequent evolution as long as the scales remain in the large-scale limit, and thus this may lead to an observable trace in the cosmic microwave background radiation.
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