Delta-N formalism for the evolution of the curvature perturbations in generalized multi-field inflation

TL;DR

This paper develops an improved delta-N formalism for analyzing the evolution of curvature perturbations in generalized multi-field inflation, incorporating non-equilibrium effects and providing a more intuitive approach.

Contribution

It introduces an enhanced delta-N formalism with a refined adiabatic field definition for generalized kinetic terms, simplifying the analysis of curvature perturbations in multi-field inflation models.

Findings

Consistent with standard kinetic term calculations

Simplifies the evolution equations for curvature perturbations

Discusses significance of non-equilibrium corrections

Abstract

The delta-N formalism is considered to calculate the evolution of the curvature perturbation in generalized multi-field inflation models. The result is consistent with the usual calculation of the standard kinetic term. For the calculation of the generalized kinetic term, we improved the definition of the adiabatic field. Our calculation improves the usual calculation of the evolution of the curvature perturbations based on the field equations and the perturbations, giving a very simple and intuitive argument for the evolution equations in terms of the perturbations of the inflaton velocity. Significance of non-equilibrium corrections are also discussed, which is caused by the small-scale (decaying) inhomogeneities. This formalism based on the modulated inflation scenario (i.e., calculation based on the perturbations related to the inflaton velocity) provides a powerful tool for investigating the signature of moduli that may appear in string theory.