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

TL;DR

This paper derives a general formula for the three-point correlation function of scalar non-Gaussianities in Horndeski theories, applicable to any shape, and explores their characteristics and dominance in specific models.

Contribution

It provides a comprehensive bispectrum expression valid for all shapes in Horndeski theories, extending previous work limited to specific configurations.

Findings

Bispectrum valid for any shape of non-Gaussianities.

In the squeezed limit, the consistency relation matches standard inflation.

Orthogonal and enfolded shapes can dominate over equilateral in certain models.

Abstract

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.