Non-Gaussian inflationary shapes in $G^3$ theories beyond Horndeski

TL;DR

This paper investigates the signatures of generalized Horndeski theories beyond standard models on inflationary non-Gaussianities, showing that complex interactions simplify to known shapes due to fundamental stability and covariance constraints.

Contribution

It demonstrates that the leading bispectrum in $G^3$ theories reduces to known shapes, revealing a universal behavior linked to stability and covariance conditions.

Findings

Bispectrum reduces to two known $k$-inflationary shapes.

Complex cubic interactions simplify due to stability constraints.

Behavior likely extends beyond cubic order due to fundamental theory requirements.

Abstract

We consider the possible signatures of a recently introduced class of healthy theories beyond Horndeski models on higher-order correlators of the inflationary curvature fluctuation. Despite the apparent large number and complexity of the cubic interactions, we show that the leading-order bispectrum generated by the Generalized Horndeski (also called $G^3$) interactions can be reduced to a linear combination of two well known $k$-inflationary shapes. We conjecture that said behavior is not an accident of the cubic order but a consequence dictated by the requirements on the absence of Ostrogradski instability, the general covariance and the linear dispersion relation in these theories.