Coupling structure of multi-field primordial perturbations

TL;DR

This paper analyzes the coupling relations among perturbations in multi-field inflation models, revealing a chain structure in mode couplings controlled by kinematic quantities and potential derivatives.

Contribution

It introduces a general formalism for deriving mode coupling relations in multi-field models and uncovers a chain structure in kinematic-controlled couplings.

Findings

Coupling relations can be reduced using background equations and derivatives.

Two categories of couplings: kinematic-controlled and potential-derivative-controlled.

Kinematic couplings exhibit a chain structure, linking neighboring modes.

Abstract

We investigate the coupling relations among perturbations in general multi-field models. We derived the equations of motion for both background and perturbations in a general basis. Within this formalism, we revisit the construction of kinematic orthogonal normal vectors using the successive time derivatives of the background field velocity. We show that the coupling relations among modes in this kinematic basis can be reduced, by employing the background equations of motion for the scalar fields and their high order time derivatives. There are two typical features in the field space: inflationary trajectory and geometry of the potential. Correspondingly, the couplings among modes fall into two categories: one is controlled only by the kinematic quantities, the other involves high order derivatives of the potential. Remarkably, the couplings of the first category, i.e. controlled by the kinematic quantities only, show a "chain" structure. That is, each mode is only coupled to its two neighbour modes.