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

We study the bispectrum of 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 density perturbations. We find that the leading-order kernel 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 is because our model, which may be equipped with the Vainshtein mechanism, includes only one simple function that describes mode couplings of the nonlinear interactions. This feature 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.