Large primordial trispectra in general single field inflation

We compute the large scalar four-point correlation functions in general single field inflation models, where the inflaton Lagrangian is an arbitrary function of the inflaton and its first derivative. We find that the leading order trispectra have four different shapes determined by three parameters. We study features in these shapes that can be used to distinguish among themselves, and between them and the trispectra of the local form. For the purpose of data analyses, we give two simple representative forms for these equilateral trispectra. We also study the effects on the trispectra if the initial state of inflation deviates from the standard Bunch-Davies vacuum.