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

TL;DR

This paper derives higher-order actions for multi-field DBI-inflation perturbations using a Lorentz boost approach, revealing unique non-Gaussian features in the four-point function that can differentiate it from single-field models.

Contribution

It introduces a Lorentz boost method to obtain higher-order actions in multi-field DBI-inflation and analyzes the resulting non-Gaussianity, especially the trispectrum.

Findings

Lorentz boost reproduces third- and fourth-order actions.

Symmetry between adiabatic and entropy modes at third order.

Distinct momentum dependence in the four-point function for multi-field models.

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.