Polarized primordial gravitational waves in the ghost-free parity-violating gravity

The tests of parity symmetry in the gravitational interaction is an attractive issue in gravitational-wave astronomy. In the general theories of gravity with parity violation, one of the fundamental results is that primordial gravitational waves (PGWs) produced during slow-roll inflation is circularly polarized. In this article, we investigate the polarization of PGWs in the recently proposed ghost-free parity-violating gravity, which generalizes Chern-Simons gravity by including higher derivatives of the coupling scalar field. For this purpose, we first construct the approximate analytical solution to the mode function of the PGWs during slow-roll inflation by using the uniform asymptotic approximation. With the approximate solution, we explicitly calculate the power spectrum and the corresponding circular polarization of the PGWs analytically, and find that the contributions of the higher derivatives of the coupling scalar field to the circular polarization are of the same order of magnitude as that of Chern-Simons gravity. The degree of circular polarization of PGWs is suppressed by the energy scale of parity violation in gravity, which is unlikely to be detected using only the two-point statistics of future cosmic microwave background data.