Shapes of primordial non-Gaussianities in the Horndeski's most general scalar-tensor theories

In the Horndeski's most general scalar-tensor theories, we derive the three-point correlation function of scalar non-Gaussianities generated during single-field inflation in the presence of slow-variation corrections to the leading-order term. Unlike previous works, the resulting bispectrum is valid for any shape of non-Gaussianities. In the squeezed limit, for example, this gives rise to the same consistency relation as that derived by Maldacena in standard single-field slow-roll inflation. We estimate the shape close to the squeezed one at which the effect of the term inversely proportional to the scalar propagation speed squared begins to contribute to the bispectrum. We also show that the leading-order bispectrum can be expressed by the linear combination of two convenient bases whose shapes are highly correlated with equilateral and orthogonal types respectively. We present concrete models in which the orthogonal and enfolded shapes can dominate over the equilateral one.