Primordial non-Gaussianities of gravitational waves beyond Horndeski

TL;DR

This paper analyzes the primordial non-Gaussianities of gravitational waves within a broad class of scalar-tensor theories, revealing the effects of modifications beyond Horndeski on tensor non-Gaussianities and their potential observational signatures.

Contribution

It provides an analytical computation of tensor 3-point functions in theories beyond Horndeski, identifying the impact of modified dispersion relations on non-Gaussian features.

Findings

Only one cubic term generates squeezed non-Gaussianity, with a universal amplitude.

Additional cubic interactions produce peaks at equilateral configurations.

Modified dispersion relations cause mild configuration-dependent changes in 3-point functions.

Abstract

We clarify the features of primordial non-Gaussianities of tensor perturbations in Gao's unifying framework of scalar-tensor theories. The general Lagrangian is given in terms of the ADM variables so that the framework maintains spatial covariance and includes the Horndeski theory and Gleyzes-Langlois-Piazza-Vernizzi (GLPV) generalization as specific cases. It is shown that the GLPV generalization does not give rise to any new terms in the cubic action compared to the case of the Horndeski theory, but four new terms appear in more general theories beyond GLPV. We compute the tensor 3-point correlation functions analytically by treating the modification to the dispersion relation as a perturbation. The relative change in the 3-point functions due to the modified dispersion relation is only mildly configuration-dependent. When the effect of the modified dispersion relation is small, there is only a single cubic term generating squeezed non-Gaussianity, which is the only term present in general relativity. The corresponding non-Gaussian amplitude has a fixed and universal feature, and hence offers a "consistency relation" for primordial tensor modes in a quite wide class of single-field inflation models. All the other cubic interactions are found to give peaks at equilateral shapes.