Stability of a Viable Non-Minimal Bounce

The main difficulties in constructing a viable early Universe bouncing model are: to bypass the observational and theoretical no-go theorem, to construct a stable non-singular bouncing phase, and perhaps, the major concern of it is to construct a stable attractor solution which can evade the Belinsky–Khalatnikov–Lifshitz (BKL) instability as well. In this article, in the homogeneous and isotropic background, we extensively study the stability analysis of the recently proposed viable non-minimal bouncing theory in the presence of an additional barotropic fluid and show that, the bouncing solution remains stable and can evade BKL instability for a wide range of the model parameter. We provide the expressions that explain the behavior of the Universe in the vicinity of the required fixed point i.e., the bouncing solution and compare our results with the minimal theory and show that ekpyrosis is the most stable solution in any scenario.

Attractor behaviour of holographic inflation model for inverse cosine hyperbolic potential

We study a model of tachyon inflation and its attractor solution in the framework of holographic cosmology. The model is based on a holographic braneworld scenario with a D3-brane located at the holographic boundary of an asymptotic ADS5 bulk. The tachyon field that drives inflation is represented by a Dirac-Born-Infeld (DBI) action on the brane. We examine the attractor trajectory in the phase space of the tachyon field for the case of inverse cosine hyperbolic tachyon potential.

Interacting vacuum at infinity

We apply the central extension technique of Poincaré to dynamics involving an interacting mixture of pressureless matter and vacuum near a finite-time singularity. We show that the only attractor solution on the circle of infinity is the one describing a vanishing matter-vacuum model at early times.

Templates of Two Foliated Attractors — Lorenz and Chen Systems

A chaotic attractor solution of the Lorenz system [Lorenz, 1963] with foliated structure is topologically characterized. Its template permits to both summarize the organization of its periodic orbits and detail the topology of the solution as a branched manifold. A template of an attractor solution of the Chen system [Chen & Ueta, 1999] with a similar foliated structure is also established.

COSMOLOGICAL DYNAMICS OF MODIFIED GRAVITY WITH A NONMINIMAL CURVATURE-MATTER COUPLING

We perform a phase space analysis of a nonminimally coupled modified gravity theory with the Lagrangian density of the form [Formula: see text], where f1(R) and f2(R) are arbitrary functions of the curvature scalar R and [Formula: see text] is the matter Lagrangian density. We apply the dynamical system approach to this scenario in two particular models. In the first model we assume f1(R) = 2R with a general form for f2(R) and set favorable values for effective equation of state parameter which is related to the several epochs of the cosmic evolution and study the critical points and their stability in each cosmic eras. In the second case, we allow the f1(R) to be an arbitrary function of R and set f2(R) = 2R. We find the late-time attractor solution for the model and show that this model has a late-time accelerating epoch and an acceptable matter era.

Phase space analysis of interacting dark energy in f(T) cosmology

In this paper, we examine the interacting dark energy model in f(T) cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form f(T) = β√T. We show that there is one attractor solution to the dynamical equation of f(T) Friedmann equations. Further we investigate the stability in phase space for a general f(T) model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet u* = (c − 1)v* in the phase space, spanned by coordinates (u, v, Ω, T). From this critical sheet, we conclude that the coupling between the dark energy and matter c ∈ (−2, 0).

ATTRACTOR SOLUTION IN COUPLED YANG–MILLS FIELD DARK ENERGY MODELS

We investigate the attractor solution in the coupled Yang–Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows that, if the attractor solution exists, the equation of state of dark energy must evolve from wy > 0 to wy ≤ -1, which is slightly suggested by the observation. At the same time, the total equation of state in the attractor solution is w tot = -1, the universe is a de Sitter expansion, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.