https://doi.org/10.1140/epjc/s10052-021-09185-7
Regular Article - Theoretical Physics
Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models
1
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
2
Departamento de Física, Universidad de Santiago de Chile, Avenida Ecuador 3493, Santiago, Chile
3
Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso, Av. Brasil 2950, Valparaiso, Chile
Received:
10
February
2021
Accepted:
25
April
2021
Published online:
12
May
2021
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index 
for locally rotationally symmetric (LRS) Bianchi III metric and open Friedmann–Lemaître–Robertson–Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic index late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution. For open FLRW metric late-time attractors are a matter dominated FLRW universe and Milne solution. With this approach, oscillations entering nonlinear system through Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble factor H – acting as a time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behaviour.
The original online version of this article was revised. The acknowledgment was replaced and the correct acknowledgment reads as follows: The research of Genly Leon and Esteban González was funded by Agencia Nacional de Investigación y Desarrollo-ANID through the program FONDECYT Iniciación grant no. 11180126. Alfredo D. Millano was supported by Agencia Nacional de Investigación y Desarrollo - ANID - Subdirección de Capital Humano/Doctorado Nacional/año 2020- folio 21200837. Claudio Michea was supported by Agencia Nacional de Investigación y Desarrollo - ANID - Subdirección de Capital Humano/Doctorado Nacional/año 2021- folio 21211604. Vicerrectoría de Investigación y Desarrollo Tecnológico at Universidad Católica del Norte is anknowleged by finacial support. Genly Leon thanks Bertha Cuadros-Melgar for her useful comments. Ellen de los Milagros Fernández Flores is acknowledged for proofreading this manuscript and improving the English. We thank anonymous referee for his/her comments which have helped us improve our work. The original article has been corrected.
An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-021-09909-9.
Copyright comment corrected publication 2021
© The Author(s) 2021. corrected publication 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
