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

TL;DR

This work extends multi-field DBI inflation to include NS-NS and R-R bulk form fields and a U(1) gauge field on the brane. It shows that scalar perturbations are unchanged by these bulk fields at second and third order due to exact cancellations, while vector modes may be affected only if the dilaton/axion vary. The analysis reinforces that equilateral non-Gaussianities persist with reduced amplitude in multi-field cases, and that gravitational-wave constraints are relaxed when entropy-to-adiabatic transfer is active, enabling compatibility with observations. Overall, the results support the viability of ultra-violet multi-field DBI inflation in realistic flux compactifications and clarify when bulk-fields influence cosmological perturbations.

Abstract

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.