Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology

Abstract Using the dynamical system theory we show that the Friedmann–Robertson–Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov–Takens normal form. The equation of state parameter, $$\omega $$ ω ,...

Full description

Bibliographic Details
Main Authors: Asmaa Abdel Azim, Adel Awad, E. I. Lashin
Format: Article
Language:English
Published: SpringerOpen 2020-09-01
Series:European Physical Journal C: Particles and Fields
Online Access:http://link.springer.com/article/10.1140/epjc/s10052-020-8384-x
_version_ 1818492054897950720
author Asmaa Abdel Azim
Adel Awad
E. I. Lashin
author_facet Asmaa Abdel Azim
Adel Awad
E. I. Lashin
author_sort Asmaa Abdel Azim
collection DOAJ
description Abstract Using the dynamical system theory we show that the Friedmann–Robertson–Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov–Takens normal form. The equation of state parameter, $$\omega $$ ω , the bulk viscosity coefficient, $$\xi $$ ξ , and the cosmological constant, $$\Lambda $$ Λ , define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters $$\omega , \Lambda $$ ω , Λ and $$\xi $$ ξ . The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability is discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.
first_indexed 2024-12-10T17:38:27Z
format Article
id doaj.art-87002c3cc1f44204a8d1bfd5ea827db8
institution Directory Open Access Journal
issn 1434-6044
1434-6052
language English
last_indexed 2024-12-10T17:38:27Z
publishDate 2020-09-01
publisher SpringerOpen
record_format Article
series European Physical Journal C: Particles and Fields
spelling doaj.art-87002c3cc1f44204a8d1bfd5ea827db82022-12-22T01:39:27ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522020-09-0180913410.1140/epjc/s10052-020-8384-xDegenerate Bogdanov–Takens bifurcations in a bulk viscous cosmologyAsmaa Abdel Azim0Adel Awad1E. I. Lashin2Department of Physics, Faculty of Science, Ain Shams UniversityDepartment of Physics, Faculty of Science, Ain Shams UniversityDepartment of Physics, Faculty of Science, Ain Shams UniversityAbstract Using the dynamical system theory we show that the Friedmann–Robertson–Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov–Takens normal form. The equation of state parameter, $$\omega $$ ω , the bulk viscosity coefficient, $$\xi $$ ξ , and the cosmological constant, $$\Lambda $$ Λ , define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters $$\omega , \Lambda $$ ω , Λ and $$\xi $$ ξ . The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability is discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.http://link.springer.com/article/10.1140/epjc/s10052-020-8384-x
spellingShingle Asmaa Abdel Azim
Adel Awad
E. I. Lashin
Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology
European Physical Journal C: Particles and Fields
title Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology
title_full Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology
title_fullStr Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology
title_full_unstemmed Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology
title_short Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology
title_sort degenerate bogdanov takens bifurcations in a bulk viscous cosmology
url http://link.springer.com/article/10.1140/epjc/s10052-020-8384-x
work_keys_str_mv AT asmaaabdelazim degeneratebogdanovtakensbifurcationsinabulkviscouscosmology
AT adelawad degeneratebogdanovtakensbifurcationsinabulkviscouscosmology
AT eilashin degeneratebogdanovtakensbifurcationsinabulkviscouscosmology