Parity Violation in Graviton Non-gaussianity

TL;DR

The paper develops a helicity-based formalism to compute graviton non-Gaussianity from parity-violating Weyl cubic interactions during inflation. It shows that exact de Sitter spacetime exhibits no parity-violating bispectrum, while slow-roll inflation induces a parity-violating signal proportional to the slow-roll parameter $\epsilon$, with left- and right-handed bispectra of equal magnitude and opposite sign. The results imply that parity-violating graviton non-Gaussianity could be probed via CMB bispectra such as $\langle TTB\rangle$, $\langle TEB\rangle$, and $\langle EEB\rangle$, and they offer a tool for connecting gravitational correlators to stress-tensor correlators in holography. The framework is applicable to broader EFT inflationary setups and may reveal UV completion effects in gravity through observable signatures.

Abstract

We study parity violation in graviton non-gaussianity generated during inflation. We develop a useful formalism to calculate graviton non-gaussianity. Using this formalism, we explicitly calculate the parity violating part of the bispectrum for primordial gravitational waves in the exact de Sitter spacetime and prove that no parity violation appears in the non-gaussianity. We also extend the analysis to slow-roll inflation and find that the parity violation of the bispectrum is proportional to the slow-roll parameter. We argue that parity violating non-gaussianity can be tested by the CMB. Our results are also useful for calculating three-point function of the stress tensor in the non-conformal field theory through the gravity/field theory correspondence.