Testing a two field inflation beyond the slow-roll approximation

We consider a model of two field inflation, containing an ordinary scalar field and a Dirac-Born-Infeld (DBI) field. We work beyond the slow-roll approximation, but we assume a separable Hubble parameter. We then derive the form of potential in this framework and study the spectrum of the primordial perturbations in detail. We also study the amplitude of the non-Gaussianity of the primordial perturbations both in equilateral and orthogonal configurations in this setup. We test the model with recent observational data and find some constraints on the model parameters. Our study shows that for some ranges of the DBI parameter, the model is consistent with observations, and it is also possible to have large non-Gaussianity which would be observable by future improvements in experiments.