Interacting dark energy: Dynamical system analysis

Golchin, Hanif; Jamali, Sara; Ebrahimi, Esmaeil

doi:10.1142/s0218271817500985

Cited by 8 publications

(6 citation statements)

References 52 publications

(40 reference statements)

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“…For example Setare & Vagenas (2009) considered Q ∝ (ρ m + ρ de )H and Karwan (2008) generalised this coupling to Q ∝ H (αρ de + βρ m ). Later delivered a dynamical analysis for the coupling Q ∝ Γρ de , assuming both Γ being a constant and a generic function of H. Other couplings have been studied by Mahata & Chakraborty (2015a) who considered Q ∝ ρ m ρ de /H and Q ∝ Hρ de , and by Golchin et al (2017) who investigated several non-linear interactions.…”

Section: Holographic Dark Energymentioning

confidence: 99%

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Dynamical systems applied to cosmology: Dark energy and modified gravity

et al. 2018

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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 there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.

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Section: Holographic Dark Energymentioning

confidence: 99%

“…In particular the so called ghost DE model which exploits the Veneziano ghost from QCD to define a DE energy density evolution characterised by ρ de ∝ H or ρ de ∝ H + H 2 . The cosmological dynamics of these models has been studied by Golchin et al (2017).…”

Section: Holographic Dark Energymentioning

confidence: 99%

Dynamical systems applied to cosmology: Dark energy and modified gravity

et al. 2018

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“…Case I: Linear Interaction (Q = Hρ tot ) [83] The set of autonomous differential equation in the case of linear interaction stated above would be:…”

Section: Stability Analysismentioning

confidence: 99%

“…For interaction, the dimensionless variables have not been tickled. Taking interaction Q between matter and dark energy, the continuity equations read, ρr + 4Hρ r = 0, ρ m + 3Hρ m = Q and ρΛ = −Q (30) Case I: Linear Interaction (Q = Hρ tot ) [83] The set of autonomous differential equation in the case of linear interaction stated above would be:…”

Section: Stability Analysismentioning

confidence: 99%

Stability analysis for cosmological models in f(R) gravity using dynamical system analysis

Shah

Samanta

2019

Eur. Phys. J. C

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Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to Einstein's theory of gravity, theories which include higher order curvature invariant, and specifically the class of f (R) theories, have received several acknowledgments. In our current work we try to understand the late time acceleration of the universe by modifying the geometry of the space and using dynamical system analysis. The use of this technique allows to understand the behavior of the universe under several circumstances. Apart from that we study the stability properties of the critical point and acceleration phase of the universe which could then be analyzed with observational data. We consider a particular model f (R) = R − µR c (R/R c ) p with 0 < p < 1, µ, R c > 0 for the study. As a first case we consider the matter and radiation component of the universe with an assumption of no interaction between them. Later, as a second case we take matter, radiation and dark energy (cosmological constant) where study on effects of linear, non-linear and no interaction between matter and dark energy is considered and results have been discussed in detail.

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“…linear stability theory, center manifold, Liapunov function, Poincaré sphere and behavior at infinity etc. In 2015, N. Mahata [13] studied Interacting Holographic Dark Energy model with great details in cosmological point of view and analyzed some hyperbolic critical points (CPs) by Hartman-Grobman theorem and in 2017, Hanif Golchin [49] analyzed Interacting HDE model by dynamical system analysis with different interaction terms. In our paper we reconstruct the autonomous system [13] so that the system can be C ∞ (R 2 ) and analyze all the CPs by center manifold and Liapunov function.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of an interacting holographic dark energy model

Mishra

Chakraborty

2019

Mod. Phys. Lett. A

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The present work deals with dynamical system analysis of Holographic Dark Energy 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 Liapunov function method. Possible bifurcation scenarios have also been explained. 98.80.Cq, 95.35.+d, 95.36.+x, 0.Ud, 6402.1.60.Fr,

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Interacting dark energy: Dynamical system analysis

Cited by 8 publications

References 52 publications

Dynamical systems applied to cosmology: Dark energy and modified gravity

Dynamical systems applied to cosmology: Dark energy and modified gravity

Stability analysis for cosmological models in f(R) gravity using dynamical system analysis

Stability analysis of an interacting holographic dark energy model

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