الفهرس 
Introduction to CosmologyOnly 14 pages are availabe for public view
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Abstract
Most of the physical phenomena can be described by non-linear dynamical systems. One can get exact solutions for some of the simplest non-linear dynamical systems but most of the non-linear dynamical systems have no exact solutions. Also, even if the system has exact solutions, it is too complicated to fully analyze the exact solutions because of the dependence of the solution behavior on the values of the system parameters, and the initial values of the variables. The dynamical system theory is providing us with powerful tools to analyze complicated non-linear dynamical systems qualitatively. One can use the dynamical system technique to attain all the different qualitative solutions for such a non-linear dynamical system like for example the standard cosmological models (Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) cosmological models).
In this work, we present a complete dynamical study for a viscous Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) cosmological model in the presence of a cosmological constant. For the sake of clarification, our investigation is carried out in three different stages. In the first stage, we only consider ω (the equation of the state parameter) to be non-vanishing, and then Λ (the cosmological constant) is included while finally ξ (the bulk viscosity coefficient) is introduced.
Viscous fluid FLRW cosmological models could be represented by twodimensional (planer) dynamical systems, where the system variables are Hubble’s parameter H and mass density ρ. Thus, in chapter 2, we explained in detail the essential dynamical tools for analyzing a planner dynamical system as well as the analysis of one-dimensional dynamical systems in order to form a solid understanding for important subjects like phase space, classification and stability of the fixed points, normal forms, and bifurcations.
In chapter 3, essential dynamical tools are applied to the perfect fluid FLRW cosmological dynamical system. Also, in order to enhance our understanding of the phase portraits which display all the different qualitative solutions. Analytical solutions for each different qualitative solution of the scale factor are attained. In chapter 4, we apply the dynamical tools to FLRW cosmological models dominated by a single perfect fluid in the presence of a cosmological constant. Then, we apply the dynamical tools to study the effect of a constant bulk viscous coefficient. For these three previous stages, phase portraits are displayed, the fixed points are discussed. The dependence of the stability of the fixed points upon the cosmological parameters is illustrated through appropriate bifurcation diagrams. The behavior at infinity is discussed through getting the corresponding compact phase portraits using Poincare’s sphere technique.
We showed that the cosmological model of a viscous fluid with the presence of cosmological constant is equivalent to a degenerate Bogdanov-Takens normal form. The necessary parameters for unfolding the degenerate BogdanovTakens system are ω, Λ, and ξ.
The structural stability issue is discussed. It is found that the existence of a non-vanishing bulk viscous coefficient guarantees that there is a finite number of fixed points, and there are no periodic orbits. Despite that these two criteria are key points for a structurally stable two-dimensional dynamical system, the bulk viscous model is not structurally stable because not all the criteria of the structural stability are satisfied.
Also, we studied the effect of a varying viscosity coefficient, but for this case, we limited our study only on the spatially flat universe which could be represented by a one-dimension dynamical system where the system variable is Hubble’s parameter. It is found that this model can provide us with a non-singular solution interpolates between an inflation point and a late-time acceleration point.