Inflationary perturbations with multiple scalar fields

TL;DR

This paper derives analytical expressions for scalar perturbations during multi-field inflation, accounting for non-minimal kinetic terms and field couplings, with numerical illustration using a quadratic potential.

Contribution

It extends slow-roll inflation perturbation theory to multiple fields with non-trivial kinetic terms, providing new analytic solutions and insights into multi-field effects.

Findings

Analytic expression for gravitational potential correlator.

Multi-field effects can contribute at leading order.

Numerical example with quadratic potential supports the theory.

Abstract

The calculation of scalar gravitational and matter perturbations during multiple-field inflation valid to first order in slow roll is discussed. These fields may be the coordinates of a non-trivial field manifold and hence have non-minimal kinetic terms. A basis for these perturbations determined by the background dynamics is introduced, and the slow-roll functions are generalized to the multiple-field case. Solutions for a perturbation mode in its three different behavioural regimes are combined, leading to an analytic expression for the correlator of the gravitational potential. Multiple-field effects caused by the coupling to the field perturbation perpendicular to the field velocity can even contribute at leading order. This is illustrated numerically with an example of a quadratic potential. (The material here is based on previous work by the authors presented in hep-ph/0107272.)