Lorentz boost and non-Gaussianity in multi-field DBI-inflation

TL;DR

The paper addresses non-Gaussianity in multi-field DBI-inflation, focusing on the trispectrum as a discriminant from single-field models. It introduces a Lorentz-boost framework to obtain the leading third- and fourth-order actions and computes the leading slow-roll, small-$c_s$ four-point function from intrinsic fourth-order contact interactions. The authors find a symmetry between adiabatic and entropy modes at cubic order, preserved by the boost, but broken at quartic order by intrinsic rest-frame terms and Hamiltonian–Lagrangian differences, yielding distinct momentum shapes for adiabatic, entropy, and mixed trispectra. Consequently, the curvature perturbation trispectrum can potentially distinguish multi-field DBI-inflation from its single-field counterpart, with observational implications for Planck-like data and future surveys.

Abstract

We show that higher-order actions for cosmological perturbations in the multi-field DBI-inflation model are obtained by a Lorentz boost from the rest frame of the brane to the frame where the brane is moving. We confirm that this simple method provides the same third- and fourth- order actions at leading order in slow-roll and in the small sound speed limit as those obtained by the usual ADM formalism. As an application, we compute the leading order connected four-point function of the primordial curvature perturbation coming from the intrinsic fourth-order contact interaction in the multi-field DBI-inflation model. At the third order, the interaction Hamiltonian arises purely by the boost from the second-order action in the rest frame of the brane. The boost acts on the adiabatic and entropy modes in the same way thus there exists a symmetry between the adiabatic and entropy modes. But at fourth order this symmetry is broken due to the intrinsic fourth-order action in the rest frame and the difference between the Lagrangian and the interaction Hamiltonian. Therefore, contrary to the three-point function, the momentum dependence of the purely adiabatic component and the components including the entropic contributions are different in the four-point function. This suggests that the trispectrum can distinguish the multi-field DBI-inflation model from the single field DBI-inflation model.