Covariant second-order perturbations in generalized two-field inflation
  We examine the covariant properties of generalized models of two-field
inflation, with non-canonical kinetic terms and a possibly non-trivial field
metric. We demonstrate that kinetic-term derivatives and covariant field
derivatives do commute in a proper covariant framework, which was not realized
before in the literature. We also define a set of generalized slow-roll
parameters, using a unified notation. Within this framework, we study the most
general class of models that allows for well-defined adiabatic and entropic
sound speeds, which we identify as the models with parallel momentum and field
velocity vectors. For these models we write the exact cubic action in terms of
the adiabatic and isocurvature perturbations. We thus provide the tool to
calculate the exact non-Gaussianity beyond slow-roll and at any scale for these
generalized models. We illustrate our general results by considering their
long-wavelength limit, as well as with the example of two-field DBI inflation.
