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 Hořava-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 $(H/M_{\ast }{)}^{n-2}(n\ge 3)$, where $H$ denotes the inflationary energy and $M_{\ast }$ the suppression mass scale of the high-order spatial derivative operators of the theory. Therefore, the next leading-order contributions come from the 3-dimensional gravitational Chern-Simons term. With some reasonable arguments, it is shown that this 3-dimensional operator is the only one that violates the parity and in the meantime has non-vanishing contributions to non-gaussianities.

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