Effects of parity violation on non-gaussianity of primordial gravitational waves in Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper investigates how parity violation influences the non-Gaussian features of primordial gravitational waves within Hořava-Lifshitz gravity, finding that high-order derivatives are suppressed and the Chern-Simons term dominates parity-violating effects.

Contribution

It demonstrates that high-order spatial derivatives have negligible effects on non-Gaussianities, highlighting the Chern-Simons term as the primary source of parity violation contributions.

Findings

Leading non-Gaussianities match those in general relativity.

High-order derivatives are suppressed by (H/M_*)^{n-2}.

Chern-Simons term is the main parity-violating contributor.

Abstract

In this paper, we study the effects of parity violation on non-gaussianities of primordial gravitational waves in the framework of Ho\v{r}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 $(H/M_*)^{n-2} \; (n \ge 3)$, 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 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.