A covariant approach to general field space metric in multi-field inflation

TL;DR

This paper develops a covariant formalism for multi-field inflation models that systematically incorporates field space geometry, enabling easier calculation of higher-order perturbations and non-Gaussianity estimates.

Contribution

It introduces a covariant approach that naturally includes field space curvature effects and explicitly derives cubic order actions for non-Gaussianity analysis.

Findings

Derived cubic order action including geometric terms

Incorporated Riemann curvature effects in perturbation analysis

Facilitated systematic higher-order calculations in multi-field inflation

Abstract

We present a covariant formalism for general multi-field system which enables us to obtain higher order action of cosmological perturbations easily and systematically. The effects of the field space geometry, described by the Riemann curvature tensor of the field space, are naturally incorporated. We explicitly calculate up to the cubic order action which is necessary to estimate non-Gaussianity and present those geometric terms which have not yet known before.