Eur. Phys. J. C (2018) 78: 169
https://doi.org/10.1140/epjc/s10052-018-5614-6

Regular Article - Theoretical Physics

Building analytical three-field cosmological models

¹ Unidade Acadêmica de Física, Universidade de Federal de Campina Grande, Campina Grande, PB, 58109-970, Brazil
² ITA-Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, 12228-900, Brazil
³ Departamento de Física, Universidade Federal da Paraíba, João Pessoa, PB, 58051-970, Brazil
⁴ Departamento de Física, Universidade Estadual da Paraíba, Campina Grande, PB, 58429-500, Brazil

^* e-mail: joaorafael@df.ufcg.edu.br

Received: 9 July 2017
Accepted: 5 February 2018
Published online: 26 February 2018

Abstract

A difficult task to deal with is the analytical treatment of models composed of three real scalar fields, as their equations of motion are in general coupled and hard to integrate. 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 with 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.