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.
