Bispectrum of cosmological density perturbations in the most general second-order scalar-tensor theory

We study the bispectrum of the matter density perturbations induced by the large scale structure formation in the most general second-order scalar-tensor theory that may possess the Vainshtein mechanism as a screening mechanism. On the basis of the standard perturbation theory, we derive the bispectrum being expressed by a kernel of the second order of the density perturbations. We find that the kernel at the leading order is characterized by one parameter, which is determined by the solutions of the linear density perturbations, the Hubble parameter and the other function specifying nonlinear interactions. This does not allow for varied behavior in the bispectrum of the matter density perturbations in the most general second-order scalar-tensor theory equipped with the Vainshtein mechanism. We exemplify the typical behavior of the bispectrum in a kinetic gravity braiding model.