Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models

Genly Leon; Esteban González; Samuel Lepe; Claudio Michea; Alfredo D. Millano

doi:10.1140/epjc/s10052-021-09580-0

2023 Impact factor 4.2

Particles and Fields

Open Access

This article has an erratum: [https://doi.org/10.1140/epjc/s10052-021-09910-2]

Eur. Phys. J. C (2021) 81: 867
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

Genly Leon¹^a, Esteban González², Samuel Lepe³, Claudio Michea¹ and Alfredo D. Millano¹

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

^a genly.leon@ucn.cl

Received: 10 February 2021
Accepted: 26 August 2021
Published online: 4 October 2021

Abstract

Scalar-field cosmologies with a generalized harmonic potential and matter with energy density $ρ_{m}$ $\rho _m$ , pressure $p_{m}$ $$p_m$$ , and barotropic equation of state (EoS) $p_{m} = (γ - 1) ρ_{m}, γ \in [0, 2]$ $p_m=(\gamma -1)\rho _m, \; \gamma \in [0,2]$ 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 $0 \leq γ \leq 2$ $0\le \gamma \le 2$ , and flat FLRW matter-dominated universe if $0 \leq γ \leq \frac{2}{3}$ $0\le \gamma \le \frac{2}{3}$ . For closed FLRW metric late-time attractors of full and averaged systems are a flat matter-dominated FLRW universe for $0 \leq γ \leq \frac{2}{3}$ $0\le \gamma \le \frac{2}{3}$ as in KS and Einstein–de Sitter solution for $0 \leq γ < 1$ $0\le \gamma <1$ . 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 $0 \leq γ < 1$ $0\le \gamma < 1$ ) too. However, for $γ \geq 1$ $\gamma \ge 1$ 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

Erratum to this article: https://doi.org/10.1140/epjc/s10052-021-09910-2

© The Author(s) 2021. corrected publication 2021

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