Introduction to the application of the dynamical systems theory in the study of the dynamics of cosmological models of dark energy
arXiv:1501.04851 · doi:10.1088/0143-0807/36/2/025008
Abstract
The theory of the dynamical systems is a very complex subject which has brought several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of the dynamical systems in cosmological settings is less known in spite of the amount of published scientific papers on this subject. In this paper a -- mostly pedagogical -- introduction to the application in cosmology of the basic tools of the dynamical systems theory is presented. It is shown that, in spite of their amazing simplicity, these allow to extract essential information on the asymptotic dynamics of a wide variety of cosmological models. The power of these tools is illustrated within the context of the so called CDM and scalar field models of dark energy. This paper is suitable for teachers, undergraduate and postgraduate students from physics and mathematics disciplines.
15 pages, 2 figures
References in corpus (5)
Cited by in corpus (10)
- Selected topics in scalar-tensor theories and beyond
- Scalar-Fluid interacting dark energy: cosmological dynamics beyond the exponential potential
- Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background
- Late time cosmic acceleration from natural infrared cutoff?
- Inflationary equilibrium configurations of scalar-tensor theories of gravity
- Reconstructing the parameter space of non-analytical cosmological fixed points
- Exploring the Evolution of Nonlinear Electrodynamics in the Universe: A Dynamical Systems Approach
- On the equivalence between Sáez-Ballester theory and Einstein-scalar field system
- A dynamical systems perspective on the thermodynamics of late-time cosmology
- Revisiting dynamics of interacting quintessence