Multi-field DBI inflation: introducing bulk forms and revisiting the
  gravitational wave constraints
  We study multi-field Dirac-Born-Infeld (DBI) inflation models, taking into
account the NS-NS and R-R bulk fields present in generic flux
compactifications. We compute the second-order action, which governs the
behaviour of linear cosmological perturbations, as well as the third-order
action, which can be used to calculate non-Gaussianities in these models.
Remarkably, for scalar-type perturbations, we show that the contributions due
to the various form fields exactly cancel in both the second- and third-order
actions. Primordial perturbations and their non-Gaussianities are therefore
unaffected by the presence of form fields and our previous results are
unmodified. We also study vector-type perturbations associated with the U(1)
gauge field confined on the D3-brane, and discuss whether their quantum
fluctuations can be amplified. Finally, we revisit the gravitational wave
constraints on DBI inflation and show that an ultra-violet DBI multi-field
scenario is still compatible with data, in contrast with the single field case,
provided there is a transfer from entropy into adiabatic perturbations.
