Effects of parity violation on non-Gaussianity of primordial gravitational waves in Horava-Lifshitz gravity

In this paper, we study the effects of parity violation on non-Gaussianities of primordial gravitational waves in the framework of the Horava-Lifshitz theory of gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear. By calculating the three-point function, we find that the leading-order contributions to the non-Gaussianities come from the usual second-order derivative terms, which produce the same bispectrum as that found in general relativity. The contributions from high-order spatial nth derivative terms are always suppressed by a factor (H/M-*)(n-2)(n >= 3), where H denotes the inflationary energy and M-* the suppression mass scale of the high-order spatial derivative operators of the theory. Therefore, the next leading-order contributions come from the three-dimensional gravitational Chern-Simons term. With some reasonable arguments, it is shown that this three-dimensional operator is the only one that violates the parity and in the meantime has nonvanishing contributions to non-Gaussianities.