Related papers: Thawing vs. Tracker Solutions: A Dynamical Systems…
Dark energy and dark matter are only indirectly measured via their gravitational effects. It is possible that there is an exchange of energy within the dark sector, and this offers an interesting alternative approach to the coincidence…
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…
Dark energy must cluster in order to be consistent with the equivalence principle. The background evolution can be effectively modelled by either a scalar field or by a barotropic fluid.The fluid model can be used to emulate perturbations…
Recently, we introduced the notion of "tracker fields," a form of quintessence which has an attractor-like solution. Using this concept, we showed how to construct models in which the ratio of quintessence to matter densities today is…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
We study three interacting dark energy models within the framework of four-dimensional General Relativity and a spatially flat Universe. In particular, we first consider two vacuum models where dark energy interacts with dark matter, while…
In this work a dynamical system approach to nonminimal coupled f(R) theories is made. The solutions of three distinct models are obtained and their stability and physical interpretation are studied to ascertain their viability as candidates…
We study the dynamical properties of tracker quintessence models using a general parametrization of their corresponding potentials, and show that there is a general condition for the appearance of a tracker behavior at early times.…
In this paper we investigate the interaction between dark matter and dark energy by considering two different interacting scenarios, i.e. the cases of constant interaction function and variable interaction function. By fitting the current…
The dynamical behaviors of two interacting dark energy models are considered. In addition to the scaling attractors found in the non-interacting quintessence model with exponential potential, new accelerated scaling attractors are also…
Current cosmological data puts increasing pressure on models of dark energy in the freezing class, e.g. early dark energy or those with equation of state $w$ substantially different from $-1$. We investigate to what extent data will…
We investigate a kind of holographic dark energy model with the future event horizon the IR cutoff and the equation of state -1. In this model, the constraint on the equation of state automatically specifies an interaction between matter…
Quintessence theories for cosmic acceleration imbue dark energy with a non-trivial dynamics that offers hope in distinguishing the physical origin of the component. We review quintessence models with an emphasis on this dynamics and discuss…
Recent data and new data analysis methods show that most probably the parameter $w$ in the equation of state of the dark energy is smaller than -1 at low redshifts. We briefly review some of the models with such a property and without…
The accelerated expansion of the Universe is one of the main discoveries of the past decades, indicating the presence of an unknown component: the dark energy. Evidence of its presence is being gathered by a succession of observational…
In this work we present a new scheme to study the tachyon dark energy model using dynamical systems analysis by considering parametrization of the equation of state(EoS) of the dark energy. Both the canonical and phantom field dynamics are…
Our work deals with the dynamical system analysis of quintessence dark energy scalar field model with exponential potential. A dynamical system analysis has been applied at the background level. Using suitable transformation of variables,…
In this paper, the notion of contraction is used to solve the trajectory-tracking problem for a class of mechanical systems. Additionally, we propose a dynamic extension to remove velocity measurements from the controller while rejecting…
Most passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the…
One of the great endeavors of the past decade has been the evaluation of different observational techniques for measuring dark energy properties and of theoretical techniques for constraining models of cosmic acceleration given cosmological…