scholarly journals Dynamical analysis and statefinder of Barrow holographic dark energy

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Qihong Huang ◽  
He Huang ◽  
Bing Xu ◽  
Feiquan Tu ◽  
Jun Chen
Keyword(s):  
Dark Energy ◽  
Turning Point ◽  
Holographic Dark Energy ◽  
Accelerated Expansion ◽  
Dynamical Analysis ◽  
Stable Model ◽  
Analysis Method ◽  
Coincidence Problem ◽  
Energy Transfers ◽  
The Stability

AbstractBased on the holographic principle and the Barrow entropy, Barrow holographic dark energy had been proposed. In order to analyze the stability and the evolution of Barrow holographic dark energy, we, in this paper, apply the dynamical analysis and statefinder methods to Barrow holographic dark energy with different IR cutoff and interacting terms. In the case of using Hubble horizon as IR cutoff with the interacting term $$Q=\frac{\lambda }{H}\rho _{m}\rho _{D}$$ Q = λ H ρ m ρ D , we find this model is stable and can be used to describe the whole evolution of the universe when the energy transfers from the pressureless matter to the Barrow holographic dark energy. When the dynamical analysis method is applied to this stable model, an attractor corresponding to an accelerated expansion epoch exists and this attractor can behave as the cosmological constant. Furthermore, the coincidence problem can be solved in this case. Then, after using the statefinder analysis method to this model, we find this model can be discriminated from the standard $$\Lambda $$ Λ CDM model. Finally, we have discussed the turning point of Hubble diagram in Barrow holographic dark energy and find the turning point does not exist in this model.

scholarly journals Barrow holographic dark energy with hubble horizon as IR cutoff

2020 ◽  
Vol 18 (01) ◽  
pp. 2150014
Author(s):  
Shikha Srivastava ◽  
Umesh Kumar Sharma
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Cosmological Parameters ◽  
Accelerated Expansion ◽  
Density Parameter ◽  
Eos Parameter ◽  
History Of ◽  
Hubble Horizon ◽  
Flrw Universe ◽  
The Stability

In this work, we propose a non-interacting model of Barrow holographic dark energy (BHDE) using Barrow entropy in a spatially flat FLRW Universe considering the IR cutoff as the Hubble horizon. We study the evolutionary history of important cosmological parameters, in particular, deceleration parameter, equation of state (EoS) parameter, the BHDE and matter density parameter, and also observe satisfactory behaviors in the BHDE model. The stability of the BHDE model has been examined by squared sound speed [Formula: see text]. In addition, to describe the accelerated expansion of the Universe, the correspondence of the BHDE model with the quintessence scalar field has been reconstructed.

scholarly journals Interacting Rényi Holographic Dark Energy in the Brans-Dicke Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Vipin Chandra Dubey ◽  
Umesh Kumar Sharma ◽  
Abdulla Al Mamon
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Cosmological Parameters ◽  
State Parameter ◽  
Accelerated Expansion ◽  
Density Parameter ◽  
Late Time ◽  
Dark Energy Density ◽  
Expansion Phase ◽  
The Stability

In this work, we construct an interacting model of the Rényi holographic dark energy in the Brans-Dicke theory of gravity using Rényi entropy in a spatially flat Friedmann-Lemaître-Robertson-Walker Universe considering the infrared cut-off as the Hubble horizon. In this setup, we then study the evolutionary history of some important cosmological parameters, in particular, deceleration parameter, Hubble parameter, equation of state parameter, and Rényi holographic dark energy density parameter in both nonflat Universe and flat Universe scenarios and also observe satisfactory behaviors of these parameters in the model. We find that during the evolution, the present model can give rise to a late-time accelerated expansion phase for the Universe preceded by a decelerated expansion phase for both flat and nonflat cases. Moreover, we obtain ω D → − 1 as z → − 1 , which indicates that this model behaves like the cosmological constant at the future. The stability analysis for the distinct estimations of the Rényi parameter δ and coupling coefficient b 2 has been analyzed. The results indicate that the model is stable at the late time.

Dynamical analysis of arbitrary dark energy and coincidence problem

2021 ◽  
Vol 36 (23) ◽  
pp. 2150159
Author(s):  
Jyotirmay Das Mandal ◽  
Mahasweta Biswas ◽  
Ujjal Debnath
Keyword(s):  
Dark Energy ◽  
Dynamical Systems ◽  
Global Stability ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Theory ◽  
Dynamical Analysis ◽  
Mathematical Form ◽  
Coincidence Problem ◽  
Nonlinear Dynamical ◽  
The Stability

This paper reviews a systematic dynamical analysis on a general form of scalar field as Dark Energy (DE) with dark matter (DM) to sort out the “cosmic coincidence” problem. Here the autonomous system of differential equations is two-dimensional (2D) as well as nonlinear. So we have utilized nonlinear dynamical theory to explain various cosmological implications of this model. Nowadays, we have noted that some works are undertaking this nonlinear systems theory. Although we have seen that most of the works are simplifying the underlying nonlinear dynamical systems similar to a linear one, that can lead to flawed conclusions about the evolution of the universe. Since an important theorem, Poincare–Bendixson theorem asserts linearization of the nonlinear system and does not give “global” stability, unlike the linear one if the dimension is more than two. Anyway, our work is different from others in this regard. Here the dimension of the system is two, and we have obtained some interesting stuffs also. We have applied the above theorem of nonlinear dynamical systems and others to find the “global” stability. This theorem offers completely different stable solutions, contrary to the prediction of linear analysis. As a result, we have obtained two fixed points; one of them is a stable “attractor” (it is attracting “node” actually), and thereafter, we have analyzed the stability. To investigate the dynamical system behavior, we have drawn different figures. These figures include vector field and a new plotting strategy (explained later). These investigations suggest a way out of the coincidence problem (or, precisely speaking, what should be the mathematical form of the term “[Formula: see text]”, which indicates interaction between DE and DM to reduce coincidence). In this scenario, if the equation of state (EoS) of DE and DM obeys [Formula: see text], then coincidence problem may be avoided.

scholarly journals Observational constraint on interacting Tsallis holographic dark energy in logarithmic Brans–Dicke theory

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Y. Aditya ◽  
Sanjay Mandal ◽  
P. K. Sahoo ◽  
D. R. K. Reddy
Keyword(s):  
Dark Energy ◽  
Graphical Representation ◽  
Holographic Dark Energy ◽  
Accelerated Expansion ◽  
Observational Constraint ◽  
Tensor Theory ◽  
Dynamical Parameters ◽  
Expansion Of The Universe ◽  
The Stability ◽  
The Universe

AbstractIn this paper, we investigate the dark energy phenomenon by studying the Tsallis holographic dark energy within the framework of Brans–Dicke (BD) scalar–tensor theory of gravity (Brans and Dicke in Phys. Rev. 124:925, 1961). In this context, we choose the BD scalar field $$\phi $$ϕ as a logarithmic function of the average scale factor a(t) and Hubble horizon as the IR cutoff ($$L=H^{-1}$$L=H-1). We reconstruct two cases of non-interacting and interacting fluid (dark sectors of cosmos) scenario. The physical behavior of the models are discussed with the help of graphical representation to explore the accelerated expansion of the universe. Moreover, the stability of the models are checked through squared sound speed $$v_s^2$$vs2. The well-known cosmological plane i.e., $$\omega _{de}-\omega ^{\prime }_{de}$$ωde-ωde′ is constructed for our models. We also include comparison of our findings of these dynamical parameters with observational constraints. It is also quite interesting to mention here that the results of deceleration, equation of state parameters and $$\omega _{de}-\omega ^{\prime }_{de}$$ωde-ωde′ plane coincide with the modern observational data.

scholarly journals Cosmic Consequences of Kaniadakis and Generalized Tsallis Holographic Dark Energy Models in the Fractal Universe

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Abdul Jawad ◽  
Abdul Malik Sultan
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Apparent Horizon ◽  
Cosmological Parameters ◽  
State Parameter ◽  
Accelerated Expansion ◽  
Energy Models ◽  
Expansion Of The Universe ◽  
The Stability ◽  
The Universe

We investigate the recently proposed holographic dark energy models with the apparent horizon as the IR cutoff by assuming Kaniadakis and generalized Tsallis entropies in the fractal universe. The implications of these models are discussed for both the interacting ( Γ = 3 H b 2 ρ m ) and noninteracting ( b 2 = 0 ) cases through different cosmological parameters. Accelerated expansion of the universe is justified for both models through deceleration parameter q . In this way, the equation of state parameter ω d describes the phantom and quintessence phases of the universe. However, the coincidence parameter r ~ = Ω m / Ω d shows the dark energy- and dark matter-dominated eras for different values of parameters. It is also mentioned here that the squared speed of sound gives the stability of the model except for the interacting case of the generalized Tsallis holographic dark energy model. It is mentioned here that the current dark energy models at the apparent horizon give consistent results with recent observations.

scholarly journals Stability analysis of an interacting holographic dark energy model

2019 ◽  
Vol 34 (19) ◽  
pp. 1950147
Author(s):  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Dark Energy ◽  
System Analysis ◽  
Holographic Dark Energy ◽  
Equilibrium Points ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lyapunov Function Method ◽  
Transformation Of Variables ◽  
The Stability ◽  
Manifold Theory

This work deals with dynamical system analysis of Holographic Dark Energy (HDE) cosmological model with different infra-red (IR)-cutoff. By suitable transformation of variables, the Einstein field equations are converted to an autonomous system. The critical points are determined and the stability of the equilibrium points are examined by Center Manifold Theory and Lyapunov function method. Possible bifurcation scenarios have also been explained.

scholarly journals INTERACTING HOLOGRAPHIC TACHYON MODEL OF DARK ENERGY

2010 ◽  
Vol 19 (05) ◽  
pp. 573-586 ◽  
Author(s):  
ALBERTO ROZAS-FERNÁNDEZ ◽  
DAVID BRIZUELA ◽  
NORMAN CRUZ
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Parameter Space ◽  
Holographic Dark Energy ◽  
Accelerated Expansion ◽  
Tachyon Field ◽  
Dark Sector ◽  
Friedmann Robertson Walker

We propose a holographic tachyon model of dark energy with interaction between the components of the dark sector. The correspondence between the tachyon field and the holographic dark energy densities allows the reconstruction of the potential and the dynamics of the tachyon scalar field in a flat Friedmann–Robertson–Walker universe. We show that this model can describe the observed accelerated expansion of our universe with a parameter space given by the most recent observational results.

scholarly journals PRESENT ACCELERATION OF THE UNIVERSE, HOLOGRAPHIC ENERGY AND BRANS–DICKE THEORY

2009 ◽  
Vol 24 (22) ◽  
pp. 1785-1792 ◽  
Author(s):  
B. NAYAK ◽  
L. P. SINGH
Keyword(s):  
Dark Energy ◽  
Power Law ◽  
Dark Energy Model ◽  
Holographic Dark Energy ◽  
Accelerated Expansion ◽  
Temporal Behavior ◽  
Holographic Dark Energy Model ◽  
Acceleration Of The Universe ◽  
Expansion Of The Universe ◽  
The Universe

The present-day accelerated expansion of the universe is naturally addressed within the Brans–Dicke theory just by using holographic dark energy model with inverse of Hubble scale as IR cutoff and power law temporal behavior of scale factor. It is also concluded that if the universe continues to expand, then one day it might be completely filled with dark energy.

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