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

Abstract

In this paper, we study the effects of parity violation on non-Gaussianities of primordial gravitational waves in the framework of the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-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 $n$th derivative terms are always suppressed by a factor $(H/{M}_{*}{)}^{n\ensuremath{-}2}(n\ensuremath{\ge}3)$, 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.