Density Perturbations in Multifield Inflationary Models

TL;DR

This work derives a closed-form analytical framework for the spectrum of long-wavelength density perturbations in two-field (and more generally multifield) inflation under slow-roll. By generalizing the single-field long-wavelength approach to include non-linear kinetic terms and an arbitrary potential V(φ, ψ), the authors obtain a compact solution for δφ, δψ, and Φ parameterized by three integration constants α, β, γ, and a background-time function F(t); γ encodes entropy perturbations and horizon crossing fixes the constants. The formalism recovers known single-field and decoupled-field results and simplifies for several potential classes, demonstrated through five concrete examples, thereby providing a practical toolkit to predict multifield perturbations and their entropic components. This advances the ability to confront multifield inflationary scenarios with CMB and large-scale structure observations by supplying explicit spectra and a clear separation of adiabatic and entropy contributions.

Abstract

We derive a closed-form, analytical expression for the spectrum of long-wavelength density perturbations in inflationary models with two (or more) inflaton degrees of freedom that is valid in the slow-roll approximation. We illustrate several classes of potentials for which this expression reduces to a simple, algebraic expression.