Abstract
We have used the dynamical system approach in order to investigate the dynamics of cosmological models of the flat Universe with a non-minimally coupled canonical and phantom scalar field and the Ratra–Peebles potential. Applying methods of the bifurcation theory we have found three cases for which the Universe undergoes a generic evolution emerging from either the de Sitter or the static Universe state and finishing at the de Sitter state, without the presence of the initial singularity. This generic class of solutions explains both the inflation and the late-time acceleration of the Universe. In this class inflation is an endogenous effect of dynamics itself.
Highlights
The main aim of cosmology is to study the structure and the evolution of the Universe at the large scale
We present the analysis of the dynamical system, describing the evolution of the universe with the dark energy as a scalar field with a potential
Within the physical region (26), the point E, representing the de Sitter universe, is a global attractor to which trajectories from points A and B are approaching
Summary
The main aim of cosmology is to study the structure and the evolution of the Universe at the large scale. We consider the phase space of cosmological models with the scalar field non-minimally coupled to the gravity to understand the full range of cosmological possibilities in epochs that are not necessarily constrained by observations. 3 we find equilibria of the dynamical system, analyse their stability properties, designate under which conditions they represent the universe with the equation of state parameter wφ = −1, find on this basis possible scenarios of the evolution from de Sitter to de Sitter universe (or else from static to de Sitter universe) – which avoids the initial singularity, and which explains the inflation and the late-time acceleration – we prepare the full analysis of bifurcations of the local stability of equilibria for these scenarios. In Appendix A a short introduction to bifurcation theory is given
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