Scalar parity-odd trispectrum from gravitational Chern-Simons interaction vertices

TL;DR

This paper investigates parity violation in the scalar trispectrum within a Chern-Simons gravity framework, showing it vanishes under standard conditions but can emerge with non-Bunch-Davies initial states.

Contribution

It introduces a detailed analysis of parity-odd trispectra from Chern-Simons gravity, including both graviton-mediated and contact diagrams, and explores conditions for non-vanishing signals.

Findings

Parity-odd trispectrum vanishes with Bunch-Davies initial conditions.

Non-Bunch-Davies initial conditions can produce a non-zero parity-odd trispectrum.

The study extends understanding of parity violation in early universe cosmology.

Abstract

In this paper, we explore parity violation in a scalar trispectrum from a dynamical Chern-Simons gravity theory. So far, a graviton-mediated diagram with two vertexes being of general relativity has been studied in this theory by taking into account the impact of a modified dispersion relation of gravitons on graviton's bulk propagators. We instead study a parity-odd trispectrum from both a graviton-mediated diagram, where one of the two vertexes originates from the Chern-Simons term, and a contact diagram by using the bulk propagators in general relativity. After computing the scalar-scalar-tensor cubic interactions and the scalar quartic ones originating from the Chern-Simons term, first we show that the resultant parity-odd trispectrum vanishes in the case of Bunch-Davies initial conditions, which is consistent with a no-go theorem for a non-vanishing parity-odd trispectrum. Then, we discuss a way to acquire a non-vanishing parity-odd trispectrum from the viewpoint of non-Bunch-Davies initial conditions.