Inflationary potentials in DBI models
  We study DBI inflation based upon a general model characterized by a
power-law flow parameter $\epsilon(\phi)\propto\phi^{\alpha}$ and speed of
sound $c_s(\phi)\propto\phi^{\beta}$, where $\alpha$ and $\beta$ are constants.
We show that in the slow-roll limit this general model gives rise to distinct
inflationary classes according to the relation between $\alpha$ and $\beta$ 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.
