Inflationary non-Gaussianities in the most general second-order scalar-tensor theories

Abstract

For very general scalar-field theories in which the equations of motion are at second order, we evaluate the three-point correlation function of primordial scalar perturbations generated during inflation. We show that the shape of non-Gaussianities is well approximated by the equilateral type. The equilateral nonlinear parameter ${f}_{\mathrm{NL}}^{\mathrm{equil}}$ is derived on the quasi-de Sitter background, where the slow-variation parameters are much smaller than unity. We apply our formula for ${f}_{\mathrm{NL}}^{\mathrm{equil}}$ to a number of single-field models of inflation---such as k-inflation, k-inflation with Galileon terms, potential-driven Galileon inflation, nonminimal coupling models (including field-derivative coupling models), and Gauss-Bonnet gravity.