Density perturbations arising from multiple field slow-roll inflation

TL;DR

This paper investigates how multiple scalar fields during slow-roll inflation influence density perturbations, introducing generalized slow-roll functions to analyze gravitational potential behavior and correlations in various field manifold geometries.

Contribution

It introduces modified slow-roll functions for multi-field inflation and analyzes their impact on gravitational perturbations and correlations in different field geometries.

Findings

Gravitational potential decouples from scalar field perturbations to varying degrees.

Correlation functions can be estimated assuming vacuum initial states.

Examples demonstrate effects on flat and curved field manifolds.

Abstract

In this paper we analyze scalar gravitational perturbations on a Robertson-Walker background in the presence of multiple scalar fields that take values on a (geometrically non-trivial) field manifold during slow-roll inflation. For this purpose modified and generalized slow-roll functions are introduced and their properties examined. These functions make it possible to estimate to what extent the gravitational potential decouples from the scalar field perturbations. The correlation function of the gravitational potential is calculated in an arbitrary state. We argue that using the vacuum state seems a reasonable assumption for those perturbations that can be observed in the CMBR. Various aspects are illustrated by examples with multiple scalar fields that take values on flat and curved manifolds.