Inflationary trispectrum for models with large non-Gaussianities

We compute the leading order contribution to the four-point function of the primordial curvature perturbation in a class of single field models where the inflationary Lagrangian is a general function of the inflaton and its first derivative. This class of models includes string motivated inflationary models such as DBI inflation. We find that the trispectrum for some range of parameters could potentially be observed in future experiments. Moreover, the trispectrum can distinguish DBI inflation from other inflation models with large non-Gaussianities which typically have a similar bispectrum. We also derive a set of consistency conditions for n-point functions of the primordial curvature perturbation in single field inflation, generalizing Maldacena's result for 3-point functions.