Parity violation in pre-inflationary bounce

The power suppression on large scale in the CMB TT-mode power spectrum might imply the occurrence of a pre-inflationary bounce. We calculate the circularly polarized gravitational wave, leaded by the gravitational Chern–Simons term universally appearing in particle physics and string theory, in the inflation model with the pre-inflationary bounce. The circularly polarized gravitational wave will induce TB- and EB-mode correlations at CMB last scatting surface. We find that if the pre-inflationary bounce actually occurs, the TB- and EB-mode correlations on large scale will be enhanced, while the BB-mode correlation on corresponding scales is suppressed