Primordial non-Gaussianity from the DBI Galileons

We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second-order field equations. This class of models generalizes the DBI Galileons in a similar way with K inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, fNLequil, can be applied to measure the amplitude of the primordial bispectrum even in the presence of the Galileon-like term although it gives a slightly different momentum dependence from K-inflation models. For the DBI Galileons, we find -0.32/cs2<fNLequil<-0. 16/cs2 and large primordial non-Gaussianities can be obtained when c_s is much smaller than 1 as in the usual DBI inflation. In G-inflation models, where a de Sitter solution is obtained without any potentials, the nonlinear parameter is given by fNLequil=4.62r⊃-2⊃/3, where r is the tensor to scalar ratio, giving a stringent constraint on the model.