Building analytical three-field cosmological models

TL;DR

This paper introduces a new methodology called the extension method to analytically construct three-field cosmological models by combining three one-field systems, facilitating the study of complex inflationary scenarios.

Contribution

The paper presents a novel extension method for building three-field models from simpler one-field systems, enabling analytical treatment of complex cosmological models.

Findings

Constructed a new three-field model demonstrating non-trivial cosmological behaviors

Provided a systematic approach to combine one-field systems into multi-field models

Applied the method to inflationary scenarios, showing its practical utility.

Abstract

A difficult task to deal with is the analytical treatment of models composed by three real scalar fields, once their equations of motion are in general coupled and hard to be integrated. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is within inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.