On the choice of entropy variables in multifield inflation

TL;DR

This paper evaluates different entropy variables in multifield inflation, clarifying which are theoretically consistent for matching inflationary and post-inflationary isocurvature modes, and warns against commonly used variables that can produce inaccurate or unphysical results.

Contribution

It identifies the proper entropy variable for accurate evolution matching in multifield inflation and highlights issues with commonly used variables that can lead to significant errors.

Findings

Commonly used entropy variables can produce errors of several orders of magnitude.

Incorrect variables may cause unphysical destabilisation effects.

Proper variable choice is crucial for accurate observational comparisons.

Abstract

We discuss the usefulness and theoretical consistency of different entropy variables used in the literature to describe isocurvature perturbations in multifield inflationary models with a generic curved field space. We clarify which is the proper entropy variable to be used to match the evolution of isocurvature modes during inflation to the one after the reheating epoch in order to compare with observational constraints. In particular, we find that commonly used variables, as the relative entropy perturbation or the one associated to the decomposition in tangent and normal perturbations with respect to the inflationary trajectory, even if more useful to perform numerical studies, can lead to results which are wrong by several orders of magnitude, or even to apparent destabilisation effects which are unphysical for cases with light kinetically coupled spectator fields.