Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation

TL;DR

This work develops a comprehensive framework for cosmological perturbations in general multi-field inflation with arbitrary kinetic terms, and applies it to multi-field DBI inflation. It derives the full second-order action, identifies a common effective sound speed $c_s$ for all perturbations in DBI, and analyzes the adiabatic-entropy mixing and its impact on the curvature perturbation, power spectra, and non-Gaussianities via a derived third-order action. In the DBI limit, entropy modes are amplified relative to adiabatic modes, and transfer between these modes can significantly modify the final curvature spectrum and the amplitude of $f_{NL}$, while keeping the equilateral shape. The paper also presents a modified consistency relation that encodes the influence of entropy transfer, highlighting potential observational signatures that could distinguish multi-field DBI scenarios from single-field models. Overall, the results provide a solid theoretical foundation for predicting CMB observables in broad multi-field k-inflation models, including the role of entropy modes in shaping primordial non-Gaussianities.

Abstract

We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multi-field extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing the dynamics of linear perturbations in the most general case. Specializing to DBI, we show that the adiabatic and entropy modes propagate with a {\it common} effective sound speed and are thus amplified at sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We also derive, in the general case, the third-order action which is useful for studying primordial non-Gaussianities generated during inflation. In the DBI case, we compute the dominant contributions to non-Gaussianities, which depend on both the adiabatic and entropy modes.