Birefringent gravitational waves and the consistency check of inflation

In this work we show that the gravitational Chern-Simons term, aside frombeing a key ingredient in inflationary baryogenesis, modifies super-horizongravitational waves produced during inflation. We compute the super-Hubblegravitational power spectrum in the slow-roll approximation and show that itsoverall amplitude is modified while its spectral index remains unchanged (atleading order in the slow-roll parameters). Then, we calculate the correctionto the tensor to scalar ratio, T/S. We find a correction of T/S which isdependent on $\cal{N}$ (more precisely quadratic in ${\cal N}$), the parametercharacterizing the amplitude of the Chern-Simons terms. In a stringy embeddingof the leptogenesis mechanism, $\cal{N}$ is the ratio between the Planck scaleand the fundamental string scale. Thus, in principle, we provide a direct probeof leptogenesis due to stringy dynamics in the Cosmic Microwave Background(CMB). However, we demonstrate that the corresponding correction of T/S is infact very small and not observable in the regime where our calculations arevalid. To obtain a sizable effect, we argue that a non-linear calculation isnecessary.Comment: 9 pages, 1 figure, RevTe