Recently, theoretical models which can produce sizeable non-Gaussianity has been extensively studied. Among them, the Dirac-Born-Infield (DBI) inflation model can produce large non-Gaussianity by the fact that the sound speed of the perturbations can be much smaller than one due to the non-trivial form of the kinetic term.
DBI inflation models are also well motivated by string theory so that the inflation fields are identified with the positions of a moving D3 brane in the six-dimensional internal space. The dynamics of the D3 brane is described by the DBI action. However, recently it has been pointed out that single field DBI inflation driven by a mobile D3 brane with large non-Gaussianity might contradict with the current WMAP data.
One way to avoid these constraints is to consider multi-field DBI models. Since the position of the brane in each compact direction is described by a scalar field, DBI inflation is naturally a multi-field inflationary model. In multi-field inflation models, the curvature perturbation is modified on large scales due to the entropy perturbation.
In this seminar, I introduce our recent work on the calculation of the bispectrum and trispectrum in multi-field DBI inflation model.