Birefringent gravitational waves and the consistency check of inflation

In this work we show that the gravitational Chern-Simons term, aside from being a key ingredient in inflationary baryogenesis, modifies superhorizon gravitational waves produced during inflation. We compute the super-Hubble gravitational power spectrum in the slow-roll approximation and show that its overall amplitude is modified while its spectral index remains unchanged (at leading order in the slow-roll parameters). Then, we calculate the correction to the tensor to scalar ratio, $T/S$. We find a correction of $T/S$ which is dependent on N (more precisely quadratic in N), the parameter characterizing the amplitude of the Chern-Simons terms. In a stringy embedding of the leptogenesis mechanism, N is the ratio between the Planck scale and the fundamental string scale. Thus, in principle, we provide a direct probe of leptogenesis due to stringy dynamics in the cosmic microwave background. However, we demonstrate that the corresponding correction of $T/S$ is in fact very small and not observable in the regime where our calculations are valid. To obtain a sizable effect, we argue that a nonlinear calculation is necessary.