The Horndeski class of models is the most general scalar-tensor theory having second-order equations of motion on any background and satisfying the weak equivalence principle. Since a new degree of freedom is introduced, we expect that the large-scale structure of the universe is affected. After a necessary introduction to the problem, in this talk I will summarize the results obtained by means of a semi-analytic approach to second-order perturbations in the context of Horndeski gravity, assuming Gaussian initial conditions. In particular, I will focus on the Dark Matter bispectrum generated at late-times by gravitational instability. I shall show that it seems unnatural to have large deviations of the bispectrum without introducing even larger deviations in the linear growth rate.

University of Barcelona