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

TL;DR

The paper analyzes parity-violating signatures in the primordial scalar trispectrum within dynamical gravitational Chern-Simons gravity. Using GR bulk propagators, it computes parity-odd contributions from both graviton-exchange and contact diagrams with CS-induced vertices, confirming that BD initial conditions produce a vanishing parity-odd trispectrum in alignment with a no-go theorem. It then shows that non-Bunch-Davies initial states can generate a nonzero parity-odd trispectrum, albeit suppressed by the CS scale $M_{CS}$ and small Bogoliubov parameters, offering a potential observational handle on parity-violating physics beyond standard inflation. Overall, the work delineates the robustness of the no-go result under conventional initial states and highlights how non-BD initial states could unlock higher-order parity-violating signals, suggesting directions for exploring enhanced configurations and mixed correlators in future studies.

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.

Figures (2)

• Figure 1: Diagram of the scalar parity-odd trispectrum mediated by graviton exchange. The external legs represent scalar propagators, while the wavy line represents the graviton propagator. The thick horizontal line is the conformal boundary $\tau_0 \rightarrow 0$, so that the graviton propagator lives in the bulk, $\tau_i <\tau_0$. The white vertex comes from the standard kinetic term of the inflaton in Eq. \ref{['eq:Lsst_GR']}. The filled vertex corresponds to the Chern-Simons coupling in Eq. \ref{['eq:sst_CS_new']}.
• Figure 2: Contact diagram contribution for the scalar parity-odd trispectrum. The black vertex can be each one of the interactions in Eqs. \ref{['eq:contactCS']} and \ref{['eq:contactGR']}.