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We study multi-field Dirac-Born-Infeld (DBI) inflation models, taking intoaccount the NS-NS and R-R bulk fields present in generic fluxcompactifications. We compute the second-order action, which governs thebehaviour of linear cosmological perturbations, as well as the third-orderaction, which can be used to calculate non-Gaussianities in these models.Remarkably, for scalar-type perturbations, we show that the contributions dueto the various form fields exactly cancel in both the second- and third-orderactions. Primordial perturbations and their non-Gaussianities are thereforeunaffected by the presence of form fields and our previous results areunmodified. We also study vector-type perturbations associated with the U(1)gauge field confined on the D3-brane, and discuss whether their quantumfluctuations can be amplified. Finally, we revisit the gravitational waveconstraints on DBI inflation and show that an ultra-violet DBI multi-fieldscenario is still compatible with data, in contrast with the single field case,provided there is a transfer from entropy into adiabatic perturbations.

Multi-field DBI inflation: introducing bulk forms and revisiting the gravitational wave constraints