https://doi.org/10.1140/epjc/s10052-021-09580-0
Regular Article - Theoretical Physics
Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models
1
Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Avda. Angamos 0610, Antofagasta, Chile
2
Dirección de Investigación y Postgrado, Universidad de Aconcagua, Pedro de Villagra 2265, 7630367, Vitacura, Santiago, Chile
3
Instituto de Física, Facultad de Ciencias, Pontificia Universidad Católica de Valparaíso, Av. Brasil 2950, Valparaiso, Chile
Received:
10
February
2021
Accepted:
26
August
2021
Published online:
4
October
2021
Scalar-field cosmologies with a generalized harmonic potential and matter with energy density 
, pressure 
, and barotropic equation of state (EoS) ![$$p_m=(\gamma -1)\rho _m, \; \gamma \in [0,2]$$](/articles/epjc/abs/2021/10/10052_2021_Article_9580/10052_2021_Article_9580_tex_eq3.png)
in Kantowski–Sachs (KS) and closed Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. We use methods from non-linear dynamical systems theory and averaging theory considering a time-dependent perturbation function D. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late-time attractors of full and time-averaged systems are two anisotropic contracting solutions, which are non-flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for 
, and flat FLRW matter-dominated universe if 
. For closed FLRW metric late-time attractors of full and averaged systems are a flat matter-dominated FLRW universe for as in KS and Einstein–de Sitter solution for 
. Therefore, a time-averaged system determines future asymptotics of the full system. Also, oscillations entering the system through Klein–Gordon (KG) equation can be controlled and smoothed out when D goes monotonically to zero, and incidentally for the whole D-range for KS and closed FLRW (if 
) too. However, for 
closed FLRW solutions of the full system depart from the solutions of the averaged system as D is large. Our results are supported by numerical simulations.
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/s10052-021-09910-2.
Copyright comment corrected publication 2021
© The Author(s) 2021. corrected publication 2021
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