On the full trispectrum in single field DBI-inflation
  We compute the tree-level connected four-point function of the primordial
curvature perturbation for a fairly general minimally coupled single field
inflationary model, where the inflaton's Lagrangian is a general function of
the scalar field and its first derivatives. This model includes K-inflation and
DBI-inflation as particular cases. We show that, at the leading order in the
slow-roll expansion and in the small sound speed limit, there are two important
tree-level diagrams for the trispectrum. One is a diagram where a scalar mode
is exchanged and the other is a diagram where the interaction occurs at a
point, i.e. a contact interaction diagram. The scalar exchange contribution is
comparable to the contact interaction contribution. For the DBI-inflation
model, in the so-called equilateral configuration, the scalar exchange
trispectrum is maximized when the angles between the four momentum vectors are
equal and in this case the amplitude of the trispectrum from the scalar
exchange is one order of magnitude higher than the contact interaction
trispectrum.
