Inflationary potentials in DBI models

We study DBI inflation based upon a general model characterized by a power-law flow parameter (φ) φ ^α and speed of sound c _s(φ) φ ^β, where α and β are constants. We show that in the slow-roll limit this general model gives rise to distinct inflationary classes according to the relation between α and β and to the time evolution of the inflaton field, each one corresponding to a specific potential; in particular, we find that the well-known canonical polynomial (large- and small-field), hybrid and exponential potentials also arise in this non-canonical model. We find that these non-canonical classes have the same physical features as their canonical analogs, except for the fact that the inflaton field evolves with varying speed of sound; also, we show that a broad class of canonical and D-brane inflation models are particular cases of this general non-canonical model. Next, we compare the predictions of large-field polynomial models with the current observational data, showing that models with low speed of sound have red-tilted scalar spectrum with low tensor-to-scalar ratio, in good agreement with the observed values. These models also show a correlation between large non-gaussianity with low tensor amplitudes, which is a distinct signature of DBI inflation with large-field polynomial potentials.