Shapes of primordial non-Gaussianities in the Horndeski'smost general scalar-tensortheories

Abstract

In the Horndeski's most general scalar-tensor theories, we derivethe three-point correlation function of scalar non-Gaussianities generatedduring single-field inflation in the presence of slow-variation correctionsto the leading-order term. Unlike previous works, the resulting bispectrumis valid for any shape of non-Gaussianities. In the squeezed limit,for example, this gives rise to the same consistency relation as thatderived by Maldacena in standard single-field slow-roll inflation.We estimate the shape close to the squeezed one at which the effectof the term inversely proportional to the scalar propagation speedsquared begins to contribute to the bispectrum. We also show that the leading-orderbispectrum can be expressed by the linear combination of two convenientbases whose shapes are highly correlated with equilateral and orthogonaltypes respectively. We present concrete models in which the orthogonaland enfolded shapes can dominate over the equilateral one.