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.

17 pages. Analysis expanded and some references added

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• Toward evading the strong coupling problem in Horndeski genesis
• Quantum Corrections in Galileons from Matter Loops
• Equivalence between Horndeski and beyond Horndeski theories and imperfect fluids
• Horndeski genesis: consistency of classical theory
• Generating cosmological perturbations in non-singular Horndeski cosmologies
• Can Horndeski Genesis be Nonpathological?
• The primordial non-Gaussianities for non-singular Horndeski cosmologies
• Unique gravitational wave signatures of GLPV scalar-tensor theories