Inflation with multiple sound speeds: a model of multiple DBI type actions and non-Gaussianities

In this letter we study adiabatic and isocurvature perturbations in the frame of inflation with multiple sound speeds involved. We suggest this scenario can be realized by a number of generalized scalar fields with arbitrary kinetic forms. These scalars have their own sound speeds respectively, so the propagations of field fluctuations are individual. Specifically, we study a model constructed by two DBI type actions. We find that the critical length scale for the freezing of perturbations corresponds to the maximum sound horizon. Moreover, if the mass term of one field is much lighter than that of the other, the entropy perturbation could be quite large and so may give rise to a growth outside sound horizon. At cubic order, we find that the non-Gaussianity of local type is possibly large when entropy perturbations are able to convert into curvature perturbations. We also calculate the non-Gaussianity of equilateral type approximately.