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

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.

arXiv comment17 pages. Analysis expanded and some references added

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