Related papers: Dynamical Systems in Cosmology: Reviewing An Alter…
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…
The present work is an example of the application of the dynamical system analysis in the context of cosmology. Here cosmic evolution is considered in the background of homogeneous and isotropic flat Friedmann-Lema\^{i}tre-Robertson-Walker…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary…
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…
Observational evidence indicating that the expansion of the universe is accelerating has surprised cosmologists in recent years. Cosmological models have sought to explain this acceleration by incorporating `dark energy', of which the…
In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe. In particular we discuss the arguments for and recent progress made towards…
Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…
Cosmology is living through fascinating times, where new observations from ground and space telescopes are questioning the established paradigm, the so-called Lambda Cold Dark Matter model. The particle nature of Dark Matter is severely…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
Motivated by the recent observations for the cosmic acceleration and the suitable evolution of the Universe provided an interaction (decay of dark energy to matter) is incorporated in a cosmological model, we study the cosmological…
Recent data advances offer the exciting prospect of a first look at whether dark energy has a dynamical equation of state or not. While formally theories exist with a constant equation of state, they are nongeneric -- Einstein's…
We apply the formalism of dynamical system analysis to investigate the evolution of interacting dark energy scenarios at the background and perturbation levels in a unified way. Since the resulting dynamical system contains the extra…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on…
Complex systems throughout Nature display structures and functions that are built and maintained, at least in part, by optimal energies flowing through them--not specific, ideal values, rather ranges in energy rate density below which…
The early cosmic inflation, when taken along with the recent observations that the universe is currently dominated by a low density vacuum energy, leads to at least two potential problems which modern cosmology must address. First, there is…
The accelerated expansion of the universe has now been confirmed by several independent observations including those of high redshift type Ia supernovae, and the cosmic microwave background combined with the large scale structure of the…
In this thesis, we used dynamical systems analysis to find the qualitative behaviour of some dark energy models. Specifically, dynamical systems analysis of quintessence scalar field models, chameleon scalar field models and holographic…