Adiabatic and Isocurvature Perturbation Projections in Multi-Field Inflation

TL;DR

This paper clarifies the distinction between field redefinitions and perturbation projections in multi-field inflation, deriving evolution equations for isocurvature perturbations without assuming specific adiabatic or isocurvature fields.

Contribution

It provides a detailed derivation of isocurvature perturbation evolution, emphasizing the difference between field redefinition and perturbation projection in multi-field inflation.

Findings

Derived evolution equations for isocurvature perturbations.

Showed consistency with covariant evolution equations.

Clarified the distinction between field redefinition and perturbation projection.

Abstract

Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the isocurvature perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the isocurvature perturbation in the flat field space limit.