Perturbations in generalized multi-field inflation

Abstract

We study the linear perturbations of multi-field inflationary models governed by a Lagrangianwhich is a general function of the scalar fields and of a global kinetic term combining theirspacetime gradients with an arbitrary field space metric. Our analysis includesk-inflation, Dirac–Born–Infeld inflation and its multi-field extensions which havebeen recently studied. For this general class of models, we calculate the action tosecond order in the linear perturbations. We decompose the perturbations into anadiabatic mode, parallel to the background trajectory, and entropy modes. Weshow that all the entropy modes propagate with the speed of light whereas theadiabatic mode propagates with an effective speed of sound. We also identify thespecific combination of entropy modes which sources the curvature perturbationon large scales. We then study in some detail the case of two scalar fields: wewrite explicitly the equations of motion for the adiabatic and entropy modes ina compact form and discuss their quantum fluctuations and primordial powerspectra.