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.
In this letter we consider a correspondence between holographic dark energy and variable modified Chaplygin gas to obtain a holographic dark energy model of the universe. The corresponding potential of the scalar field has been reconstructed which describes the modified variable Chaplygin gas. The stability of the holographic dark energy in this case is also discussed.
We discuss an interacting tachyonic dark energy model in the context of the holographic principle. The potential of the holographic tachyon field in interaction with dark matter is constructed. The model results are compared with CMB shift parameter, baryonic acoustic oscilations, lookback time and the Constitution supernovae sample. The coupling constant of the model is compatible with zero, but dark energy is not given by a cosmological constant.
We investigate the cosmological dynamics of interacting Logarithmic Entropy Corrected Holographic Dark Energy model with Cold Dark Matter. Fixed points are determined and their corresponding cosmological models are presented. Moreover, the dynamical properties of these fixed points are derived.
We present a holographic dark energy model of the universe considering modified generalized Chaplygin gas (GCG). The modified GCG behaves as an ordinary barotropic fluid in the early epoch when the universe was tiny but behaves subsequently as a $Λ$CDM model at late epoch. An equivalent model with scalar field is obtained here by constructing the corresponding potential. The holographic dark energy is identified with the modified GCG and we determine the corresponding holographic dark energy field and its potential. The stability of the holographic dark energy in this case is also discussed.
In this manuscript, we present a generalization of the interacting holographic dark energy model using the viscous generalized Chaplygin gas. We also study the model by considering a dynamical Newton's constant $G$. Then we reconstruct the potential and the dynamics of the scalar field which describe the viscous Chaplygin cosmology.
In this work, we explore the phenomenon of cosmic evolution using curved FLRW space-time bounded by apparent horizon with a specific holographic cut-off. To this end, we use the framework of Rastall gravity (RG) and universe is assumed to be consists of interacting/ non-interacting dark energy (DE) and dark matter (DM). In both scenarios, we evaluate exact solutions of the dynamical equations and constraint the holographic parameter $c^{2}(z)$ assuming a slowly varying function of red-shift during non-interacting model. For interacting model, we consider $c^{2}$ as a constant function of red-s…
We investigate the compact Kaluza-Klein cosmology in which modified holographic dark energy is interacting with dark matter. Using this scenario, we evaluate equation of state parameter as well as equation of evolution of the modified holographic dark energy. Further, it is shown that the generalized second law of thermodynamics holds without any constraint.
We examine the evolution of a holographic cosmological model with future event horizon as the infrared cut-off and dark matter and dark energy do not evolve independently $-$ there is interaction between them. The basic evolution equations are reduced to an autonomous system and corresponding phase space is analyzed.
We consider interacting holographic dark energy model in Friedmann Robertson Walker space time with positive spatial curvature and investigate the behavior of curvature parameter and dark energy density in accelerated expanding epoch. We also derive some conditions needed to cross the phantom divide line in this model.
This paper is aimed at investigating a 5D holographic dark energy in DGP-BRANE cosmology by employing a combination of Sne Ia, BAO and CMB observational data to fit the cosmological parameters in the model. We describe the dynamic of a FRW for the normal branch ($ε$ = +1) of solutions of the induced gravity brane-world model. We take the matter in 5D bulk as holographic dark energy that its holographic nature is reproduced effectively in 4D. The cosmic evolution reveals that the effective 4D holographic dark energy behaves as quintessence while taking into account the 4D cold dark matter resul…
The $f(R)$ gravity theory is considered. It is a gravitational theory that generalizes the Einstein-Hilbert action. In this context, a holographic dark energy model is studied. Tsallis non-extensive entropy is used to introduce the dark energy density based on the holographic principle. Then the Friedmann equation, deceleration parameter, and equation of state for this model are investigated.
Introducing a new infrared cut-off for the holographic dark-energy, we study the correspondence between the quintessence, tachyon, K-essence and dilaton energy density with this holographic dark energy density in the flat FRW universe. This correspondence allows to reconstruct the potentials and the dynamics for the scalar fields models, which describe accelerated expansion.
We consider a holographic dark energy model, with a varying parameter, n, which evolves slowly with time. We obtain the differential equation describing evolution of the dark energy density parameter, $Ω_d$, for the flat and non-flat FRW universes. The equation of state parameter in this generalized version of holographic dark energy depends on n.
In this work, we use the statefinder parameter diagnostic to the Holographic principal inspired dark energy models, taking into consideration, the Tsallis Holographic dark energy (THDE) model, the standard Holographic dark energy (HDE) model, and the R$\acute{e}$nyi holographic dark energy (RHDE) model. The evolutionary behaviour of first statefinder $r(z)$, second statefinder parameter $s(z)$, the statefinder parameter pairs $(r, s)$ and $(r, q)$ as well as the deceleration parameter $q(z)$ are plotted for comparison for the various parameter values of the respective dark energy models. In th…
A cosmological model of an holographic dark energy interacting with dark matter throughout a decaying term of the form $Q=3(λ_1ρ_{DE} + λ_2ρ_m) H$ is investigated. General constraint on the parameters of the model are found when accelerated expansion is imposed and we found a phantom scenarios, without any reference to a specific equation of state for the dark energy. The behavior of equation of stated for dark energy is also discussed.
We investigate the origin of holographic dark energy models which were recently proposed to explain the dark energy-dominated universe. For this purpose, we introduce the spacetime foam uncertainty of $δl \ge l_{\rm p}^αl^{α-1}$. It was argued that the case of $α=2/3$ could describe the dark energy with infinite statistics, while the case of $α=1/2$ can describe the ordinary matter with Bose-Fermi statistics. However, two cases may lead to the holographic energy density if the latter recovers from the geometric mean of UV and IR scales. Hence the dark energy with infinite statistics based on t…
The holographic dark energy (HDE) is considered to be the most promising candidate of dark energy. Its definition is originally motivated from the entropy-area relation which depends on the theory of gravity under consideration. Recently a new definition of HDE is proposed with the help of quantum corrections to the entropy-area relation in the setup of loop quantum cosmology. Using this new definition, we investigate the model of interacting dark energy and derive its effective equation of state. Finally we establish a correspondence between generalized Chaplygin gas and entropy-corrected hol…
In this paper we consider holographic dark energy model with corrected holographic energy density and show that this model may be equivalent to the modified Chaplygin gas model. Then we obtain relation between entropy corrected holographic dark energy model and scalar field models. We do these works by using choices of IR cut-off length proportional to the Hubble radius, the event horizon radius, the Ricci length, and the Granda-Oliveros length.
In this paper, we study the holographic dark energy model in non-flat universe from the statefinder viewpoint. We plot the evolutionary trajectories of the holographic dark energy model for different values of the parameter $c$ as well as for different contributions of spatial curvature, in the statefinder parameter-planes. The statefinder diagrams characterize the properties of the holographic dark energy and show the discrimination between this scenario and other dark energy models. As we show, the contributions of the spatial curvature in the model can be diagnosed out explicitly by the sta…
We discuss the connection between black hole and holographic dark energy. We examine the issue of the equation of state (EOS) for holographic energy density as a candidate for the dark energy carefully. This is closely related to the EOS for black hole, because the holographic dark energy comes from the black hole energy density. In order to derive the EOS of a black hole, we may use its dual (quantum) systems. Finally, a regular black hole without the singularity is introduced to describe an accelerating universe inside the cosmological horizon. Inspired by this, we show that the holographic …
The modified gravity is considered in the framework of the holographic dark energy. An analysis of the autonomous system, the critical points and their stability is presented. Unlike the dark energy models based on $f(R)$, it is found that working in the holographic frame enriches the possibility of accelerated and matter type points for different cosmological scenarios, making viable trajectories of successful $f(R)$ models that are not allowed without the consideration of the holographic framework. The implications for the Hu-Sawicki model are analyzed.
We have explored cold dark matter and holographic dark energy cosmological models with big rip singularity. To obtain the solution of the field equation, we have supposed that scalar expansion $θ$ is proportional to shear scalar $σ^2 $ which leads to $p_1=(p_2) ^n $, where $A_1 $, $A_2$ are metric potentials and $ n$ is constant. Big bang and Big rip singularity are investigated and analyzed the state-finder parameter. The physical and geometrical parameters of the universe are explained.
It is argued that the $c^{2}$ term that appears in the conventional formula for holographic dark energy should not be assumed constant in general. Notwithstanding, there is at least an exception, namely, when the Ricci scale is chosen as the infrared cutoff length.
We study the inflation via logarithmic entropy-corrected holographic dark energy LECHDE model with future event horizon, particle horizon and Hubble horizon cut-offs, and compare the results with those of obtained in the study of inflation by holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in HDE model. Moreover, the consistency with the observational data in LECHDE model of inflation, constrains the reheating temperature and Hubble parameter by one parameter of holographic dark energy and t…
We discuss two lagrangian interacting dark energy models in the context of the holographic principle. The potentials of the interacting fields are constructed. The models are compared with CMB distance information, baryonic acoustic oscilations, lookback time and the Constitution supernovae sample. For both models the results are consistent with a non vanishing interaction between dark sectors - with more than three standard deviations of confidence for one of them. Moreover, in both cases, the sign of coupling is consistent with dark energy decaying into dark matter, alleviating the coinciden…
Conditions needed to cross the phantom divide line in an interacting holographic dark energy model in closed Friedmann- Robertson-Walker universe are discussed. The probable relationship between this crossing and the coincidence problem is studied.
In this paper, we present a model for the late-time evolution of the universe where a dark energy-dark matter interaction is invoked. Dark energy is modeled through an holographic Ricci dark energy component. The model is embedded within an induced gravity brane-world model. For suitable choices of the interaction coupling, the big rip and little rip induced by the holographic Ricci dark energy, in a relativistic model and in an induced gravity brane-world model, are removed. In this scenario, the holographic dark energy will have a phantom-like behaviour even though the brane is asymptoticall…
In this work, we have studied accretion of dark energy (DE) onto Morris- Thorne wormhole with three different forms, namely, holographic dark energy, holographic Ricci dark energy and modified holographic Ricci dark energy . Considering the scale factor in power-law form we have observed that as the holographic dark energy accretes onto wormhole, the mass of the wormhole is decreasing. In the next phase we considered three parameterization schemes that are able to get hold of quintessence as well as phantom phases. Without any choice of scale factor we reconstructed Hubble parameter from conse…
We construct a holographic dark energy model in a braneworld setup that gravity is induced on the brane embedded in a bulk with Gauss-Bonnet curvature term. We include possible modification of the induced gravity and its coupling with a canonical scalar field on the brane. Through a perturbational approach to calculate the effective gravitation constant on the brane, we examine the outcome of this model as a candidate for holographic dark energy.
Holographic model is originated from Holographic principle. The equation of state in Holographic model and Einstein's gravity with particle horizon can be obtained as wD>-1/3 and cannot justify the expansion acceleration of the Universe. But, by using the event horizon, this model can result in the accelerating expansion in Einstein's gravity and Brans-Dicke cosmology. In this context, we study the holographic model with apparent horizon satisfying the acceleration expansion. We shall see, in the presence of interaction, phase change and transition from decelerated state to accelerated state i…
The purpose of this paper is to discuss the evolution of modified holographic dark energy with variable $G$ in non-flat Kaluza$-$Klein universe. We consider the non-interacting and interacting scenarios of the modified holographic dark energy with dark matter and obtain the equation of state parameter through logarithmic approach. It turns out that the universe remains in different dark energy eras for both cases. Further, we study the validity of the generalized second law of thermodynamics in this scenario. We also justify that the statefinder parameters satisfy the limit of $Λ$CDM model.
In this work we establish a correspondence between the tachyon, K-essence and dilaton scalar field models with the interacting entropy-corrected holographic dark (ECHD) model in non-flat FRW universe. The reconstruction of potentials and dynamics of these scalar fields according to the evolutionary behavior of the interacting ECHDE model are be done. It has been shown that the phantom divide can not be crossed in ECHDE tachyon model while it is achieved for ECHDE K-essence and ECHDE dilaton scenarios. At last we calculate the limiting case of interacting ECHDE model, without entropy-correction…
In the paper, we apply the weak gravity conjecture to the holographic quintessence model of dark energy. Three different holographic dark energy models are considered: without the interaction in the non-flat universe; with interaction in the flat universe; with interaction in the non-flat universe. We find that only in the models with the spatial curvature and interaction term proportional to the energy density of matter, it is possible for the weak gravity conjecture to be satisfied.
We study the holographic dark energy model in a generalized scalar tensor theory. In a universe filled with cold dark matter and dark energy, the effect of potential of the scalar field is investigated in the equation of state parameter. We show that for a various types of potentials, the equation of state parameter is negative and transition from deceleration to acceleration expansion of the universe is possible.
We propose an holographic quintessence and tachyon models of dark energy. The correspondence between the quintessence and tachyon energy densities with the holographic density, allows the reconstruction of the potentials and the dynamics for the quintessence and tachyon fields, in flat FRW background. The proposed infrared cut-off for the holographic energy density works for two cases of the constant $α$: for $α<1$ we reconstructed the holographic quintessence model in the region before the $ω=-1$ crossing for the EoS parameter. The cosmological dynamics for $α>1$ was also reconstructed for th…
The present work deals with a detailed study of interacting holographic dark energy model for three common choices of the interaction term. Also, two standard choices of IR cut-off, namely, Ricci length scale and radius of the event horizon are considered here. Finally, the cosmographic parameters are presented both analytically and graphically.
The paper deals with a dynamical system analysis of the cosmological evolution of an holographic dark energy (HDE) model interacting with dark matter (DM) which is chosen in the form of dust. The infrared cut-off of the holographic model is chosen as future event horizon or Ricci length scale. The interaction term between dark energy and dark matter is chosen of following three types i) proportional to the sum of the energy densities of the two dark components ii) proportional to the product of the matter energy densities and iii) proportional to dark energy density. The dynamical equations ar…
We propose in this paper an interacting holographic dark energy (IHDE) model in chameleon--tachyon cosmology by interaction between the components of the dark sectors. In the formalism, the interaction term emerges from the scalar field coupling matter lagrangian in the model rather than being inserted into the formalism as an external source for the interaction. The correspondence between the tachyon field and the holographic dark energy (HDE) densities allows to reconstruct the tachyon scalar field and its potential in a flat FRW universe. The model can show the accelerated expansion of the …
We generalize the holographic dark energy model described in Hubble length IR cutoff by assuming a slowly time varying function for holographic parameter $c^2$. We calculate the evolution of EoS parameter and the deceleration parameter as well as the evolution of dark energy density in this generalized model. We show that the phantom line is crossed from quintessence regime to phantom regime which is in agreement with observation. The evolution of deceleration parameter indicates the transition from decelerated to accelerated expansion. Eventually, we show that the GHDE with HIR cutoff can int…
In this work we explore a Holographic Dark Energy Model in a flat Friedmann-Lemaître-Robertson-Walker Universe, which contains baryons, radiation, cold dark matter and dark energy within the framework of General Relativity. Furthermore, we consider three types of phenomenological interactions in the dark sector. With the proposed model we obtained the algebraic expressions for the cosmological parameters of our interest: the deceleration and coincidence parameters. Likewise, we graphically compare the proposed model with the $Λ$CDM model.
The present work is based on the idea of an interacting framework of new holographic dark energy with cold dark matter in the background of $f(T)$ gravity. Here, we have considered the flat modified Friedmann universe for $f(T)$ gravity which is filled with new Holographic dark energy and dark matter. We have derived some cosmological parameters like Deceleration parameter, EoS parameter, State-finder parameters, Cosmographic parameters, {\it Om} parameter and graphically investigated the nature of these parameters for the above mentioned interacting scenario. The results are found to be consi…
We discuss the consequences of possible sign changes of the $Q$-function which measures the energy transference between dark energy and dark matter. We investigate this scenario from a holographic perspective to modeling the dark energy by a linear-parametrization of the equation of state parameter denoted by $ω$. By imposing the strong constraint of the second law of thermodynamics, we show that sign changes of $Q$ due to the cosmic evolution imply changes in the temperatures of dark energy and dark matter, respectively. We also discuss the phase transitions, in the past and future, experienc…
Based 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 $Q=\fracλ{H}ρ_{m}ρ_{D}$, 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…
In this letter, we investigate the validity of the generalized second law of thermodynamics of the universe bounded by the event horizon in the holographic dark energy model. The universe is chosen to be homogeneous and isotropic and the validity of the first law has been assumed here. The matter in the universe is taken in the form of non-interacting two fluid system- one component is the holographic dark energy model and the other component is in the form of dust.
Here we investigate the holographic dark energy model in the framework of FRW cosmology where the Newtonian gravitational constant,$G$, is varying with cosmic time. Using the complementary astronomical data which support the time dependency of $G$, the evolutionary treatment of EoS parameter and energy density of dark energy model are calculated in the presence of time variation of $G$. It has been shown that in this case, the phantom regime can be achieved at the present time. We also calculate the evolution of $G$- corrected deceleration parameter for holographic dark energy model and show t…
We study the Rényi holographic dark energy (RHDE) model by using the future and the particle horizons as the infrared (IR) cut-off. With the initial condition from the literature, most of the cosmological parameters are computed. Some of the results agree with the observation that the present universe is in accelerating expansion and in a phantom phase.
The energy density of the holographic dark energy is based on the area law of entropy, and thus any modification of the area law leads to a modified holographic energy density. Inspired by the entropy expression associated with the apparent horizon of a Friedmann-Robertson-Walker (FRW) Universe in DGP braneworld, we propose a new model for the holographic dark energy in the framework of DGP brane cosmology. We investigate the cosmological consequences of this new model and calculate the equation of state parameter by choosing the Hubble radius, $L = H^{-1}$, as the system's IR cutoff. Our stud…
In this work, I framed the Renyi and Tsallis Holographic Dark Energy (HDE) models within the presence of a spatially flat and isotropic FRW model filled with matter and dark energy in teleparallel gravity. The energy densities of Renyi HDE and Tsallis holographic dark energy (THDE) are increasing functions of z and validate the expanding conduct of the universe. It is worthwhile to note that for -1<z<0, the EoS parameter of Renyi HDE approaches to phantom region , while THDE confirms to Quintessence region. Further for 0<z, the EoS parameter of Renyi HDE slants to CDM model ,while THDE settles…
The some models of holographic dark energy for Randall-Sandrum brane are considered. For first class of dark energy models we take energy density in form $\sim L^{2γ-4}$ where $L$ is size of events horizon in Universe and $γ$ is parameter (Tsallis holographic energy). Analysis of observational data allows to define upper limit on value of $δ=ρ_{0}/2λ$ ($ρ_{0}$ is current energy density in the Universe and $λ$ is brane tension). Then we investigate models for which dark energy density has form $ρ_{de}=C^{2}L^{-2}-C_{1}^{2}H^{2}$ where $H$ is Hubble parameter.
In the framework of Brans-Dicke cosmology, we have studied the interacting power-law and logarithmic entropy-corrected holographic dark energy models with different cut-offs. The Brans-Dicke parameter is investigated versus the conditions for the acceleration and phantom phases to show that which entropy corrected model can exhibit acceleration with or without the phantom phase at early and present time universes. Moreover, the classical stability or instability of the interacting power-law and logarithmic entropy-corrected holographic dark energy models with different cut-offs is determined a…
Recently one of us derived the action of modified gravity consistent with the holographic and new-agegraphic dark energy. In this paper, we investigate the stability of the Lagrangians of the modified gravity as discussed in [M. R. Setare, Int. J. Mod. Phys. D 17 (2008) 2219; M. R. Setare, Astrophys. Space Sci. 326 (2010) 27]. We also calculate the statefinder parameters which classify our dark energy model.
We consider a Tsallis holographic dark energy model with interaction between dark energy and matter. The density of dark energy is taken as $ρ_d \sim 3C^2/L^{4-2γ}$, where $C$, $γ$ are constants. The event horizon is chosen as the characteristic scale $L$. The cosmological dynamics of the universe are analyzed, with special attention paid to the possibility of crossing the phantom line $w_{eff}=-1$. It is shown that for certain values of parameters this may occur not only once, but also twice.
We reconstruct $f(T)$ theories from three different holographic dark energy models in different time durations. For the HDE model, the dark energy dominated era with new setting up is chosen for reconstruction, and the radiation dominated era is chosen when the involved model changes into NADE. For the RDE model, radiation, matter and dark energy dominated time durations are all investigated. We also investigate the limitation which prevents an arbitrary choice of the time duration for reconstruction in HDE and NADE, and find that an improved boundary condition is needed for a more precise rec…
We study the dynamics of interacting holographic dark energy model in Brans-Dicke cosmology for the future event horizon and the Hubble horizon cut-offs. We determine the system of first-order differential equations for the future event horizon and Hubble horizon cut-offs, and obtain the corresponding fixed points, attractors, repellers and saddle points. Finally, we investigate the cosmic coincidence problem in this model for the future event horizon and Hubble horizon cut-offs and find that for both cut-offs and for a variety of Brans-Dicke parameters the coincidence problem is almost resolv…
In this paper, the model of holographic Chaplygin gas has been extended to two general cases: first is the case of modified variable Chaplygin gas and secondly of the viscous generalized Chaplygin gas. The dynamics of the model are expressed by the use of scalar fields and the scalar potentials.
Dark Energy models are here investigated and studied in the framework of the Chern-Simons modified gravity model. We bring into focus the Holographic Dark Energy (HDE) model with Granda-Oliveros cut-off, the Modified Holographic Ricci Dark Energy (MHRDE) model and, moreover, a model with higher derivatives of the Hubble parameter as well. The relevant expressions of the scale factor a(t) for a Friedmann-Robertson-Walker Universe are derived and studied, and in this context, the evolution of the scale factor is shown to be similar to that one displayed by the modified Chaplygin gas in two of th…
In the present work, we study the R$\acute{e}$nyi holographic dark energy model (RHDE) in a flat FRW Universe where the infrared cut-off is taken care by the Hubble horizon and also by taking three different parametrizations of the interaction term between the dark matter and the dark energy. Analyzing graphically, the behavior of some cosmological parameters in particular deceleration parameter, equation of state (EoS) parameter, energy density parameter and squared speed of sound, in the process of the cosmic evolution, is found to be leading towards the late-time accelerated expansion of th…
