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.
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 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.
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 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 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…
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…
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.
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.
The novel idea that spatial expansion of our universe can be regarded as the consequence of the emergence of space was proposed by Padmanabhan. By using of the basic law governing the emergence, which Padmanabhan called holographic equipartition, he also arrives at the Friedmann equation in a flat universe. When generalized to other gravity theories, the holographic equipartition need to be generalized with an expression of $f(ΔN,N_{sur})$. In this paper, we give general expressions of $f(ΔN,N_{sur})$ for generalized holographic equipartition which can be used to derive the Friedmann equations…
In this article we apply the holographic principle for describing in a unifying way the early and the late-time universe, when the general equation of state contains a bulk viscosity. We use the idea of a generalized cut-off holographic dark energy introduced by Nojiri and Odintsov (2006,2017), and study the evolution of the universe when the equation of state has two power-law asymptotes. Analytical expressions for the infrared cut-offs in terms of the particle horizon are obtained. The energy conservation laws as derived from the holographic point of view, are given for various forms of the …
Rényi Holographic Dark Energy (RHDE) Models has been studied in different dimensions considering a flat FRW metric, subsequently exploring the nature of evolution of different cosmological parameters. It is seen that the number of dimensions affect the evolution of the cosmological parameters and the transition of the universe from decelerating to accelerating phase. The statefinder diagnosis has been performed and it is seen that the model corresponds to the $ΛCDM$ model for the present and future universe.
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.
We investigate the accelerated expansion of the late-time universe in the Friedmann-Robertson-Walker metric with nonzero curvature, applying a holographic principle based on a generalized holographic dark energy model introduced by Nojiri and Odintsov (2005,2006). We describe the evolution of the universe using a generalized equation of state in the presence of a viscous fluid. Solutions of the gravitational equation of motions are obtained in explicit form for a constant value of the thermodynamic parameter, and for various forms of the bulk viscosity. We calculate analytic expressions for in…
By incorporating the holographic principle in a time-depending Lambda-term cosmology, new physical bounds on the arbitrary parameters of the model can be obtained. Considering then the dark energy as a purely geometric entity, for which no equation of state has to be introduced, it is shown that the resulting range of allowed values for the parameters may explain both the coincidence problem and the universe accelerated expansion, without resorting to any kind of additional structures.
We study the cosmological consequences of interacting Tsallis holographic dark energy model in the framework of the fractal universe, in which, the Hubble radius is considered as the IR cut-off. We drive the equation of state (EoS) parameter, deceleration parameter and the evolution equation for the Tsallis holographic dark energy density parameter. Our study shows that this model can describe the current accelerating Universe in both noninteracting and interacting scenarios, and also a transition occurs from the deceleration phase to the accelerated phase, at the late time. Finally, we check …
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 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…
Motivated by the work of Granda and Oliveros [L.N. Granda, A. Oliveros, Phys. Lett. B {\bf 671}, 199 (2009)], we generalize their work to the non-flat case. We study the correspondence between the quintessence, tachyon, K-essence and dilaton scalar field models with the new holographic dark energy model in the non-flat FRW universe. We reconstruct the potentials and the dynamics for these scalar field models, which describe accelerated expansion of the universe. In the limiting case of a flat universe, i.e. $k = 0$, all results given in [L.N. Granda, A. Oliveros, Phys. Lett. B {\bf 671}, 199 (…
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.
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…
We propose a cosmological scenario which describes the evolution history of the universe based on the particle creation and holographic equipartition. The model attempts to solve the inflation of the early universe and the accelerated expansion of the present universe without introducing the dark energy from the perspective of thermodynamics. Throughout the evolution of the universe, we assume that the universe always creates particles in some way and holographic equipartition is always satisfied. Further, we choose that the creation rate of particles is proportional to $H^{2}$ in the early un…
We consider the interacting holographic dark energy with new infrared cutoff (involving Hubble parameter and its derivative) in non-flat universe. In this context, we obtain the equation of state parameter which evolutes the universe from vacuum dark energy region towards quintessence region for particular values of constant parameters. It is found that this model always remains unstable against small perturbations. Further, we establish the correspondence of this model having quintessential behavior with quintessence, tachyon, K-essence and dilaton scalar field models. The dynamics of scalar …
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 …
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…
The $f(R)$ gravity models formulated in Einstein conformal frame are equivalent to Einstein gravity together with a minimally coupled scalar field. The scalar field couples with the matter sector and the coupling term is given by the conformal factor. We apply the holographic principle to such an interacting model in spatially flat and curved universes. We show that the model leads to a constant ratio of energy densities of dark matter to dark energy in a spatially flat universe. In a spatially curved universe, the ratio is not a constant and the evolution seems to be model-dependent. However,…
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…
We apply the holographic principle to the Brans-Dicke cosmology. We analyze the holographic bound in both the Jordan and Einstein frames. The holographic bound is satisfied for both the k=0 and k=-1 universe, but it is violated for the k=1 matter dominated universe.
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.
The probable trajectory of the ground state wave function of the universe arises through a quantum tunneling by gravitational instantons. We calculate the quantum tunneling rate for a $n>2$ dimensional closed Friedmann-Robertson-Walker universe with a positive cosmological constant. In four dimensions, by using of the holographic principle, the tunneling rate is related to the maximal entropy of the early universe after quantum tunneling.
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.
In this paper we deal with accretion of dark energy in the holographic dark energy model for a general non-rotating static spherically symmetric black hole. The mass of the black hole increases or decreases depending on the nature of the holographic dark energy (quintessence or phantom) as well as on some integration parameters. It is to be illustrated that the enhancement or reduction of mass of a black hole is independent of the mass or size of the black hole itself. Rather it depends only upon the radius of the event horizon of the universe. Finally, the generalized second law of thermodyna…
Holographic dark energy (HDE), presents a dynamical view of dark energy which is consistent with the observational data and has a solid theoretical background. Its definition follows from the entropy-area relation $S(A)$, where $S$ and $A$ are entropy and area respectively. In the framework of loop quantum gravity, a modified definition of HDE called "entropy-corrected holographic dark energy" (ECHDE) has been proposed recently to explain dark energy with the help of quantum corrections to the entropy-area relation. Using this new definition, we establish a correspondence between modified vari…
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 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…
Information $I$ in holographic imaging of massive particles by star-like screens is shown to represent the probability of detection based on their propagator. Results are derived for screens in the shape of a plane, cube and sphere from unitarity in the exponentially small transition probability for a detection outside. We derive $I=2πΔφ$ in $\log2$ bits for the imaging of a particle by a spherical screen at a relative de Broglie phase $Δφ$. Encoding mass, charge, angular momentum or radiation requires at minimum four bits. Minimal screens at maximal information density hereby recover Reissner…
In this paper, we investigate the validity of the generalized second law of thermodynamics of the universe in the DGP brane world.The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon or the event horizon. 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.
Author of Ref. [1], M.R. Setare (JCAP 01, 023, 2007, arXiv:hep-th/0701242), by redefining the event horizon measured from the sphere of the horizon as the system's IR cut-off for an interacting holographic dark energy model in a non-flat universe, showed that the generalized second law of thermodynamics is satisfied for the special range of the deceleration parameter. His paper includes an erroneous calculation of the entropy of the cold dark matter. Also there are some missing terms and some misprints in the equations of his paper. Here we present that his conclusion is not true and the gener…
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…
In this paper, the holographic dark energy model with new infrared cut-off proposed by Granda and Oliveros has been investigated in spatially non flat universe. The dependency of the evolution of equation of state, deceleration parameter and cosmological evolution of Hubble parameter on the parameters of new HDE model are calculated. Also, the statefinder parameters $r$ and $s$ in this model are derived and the evolutionary trajectories in $s-r$ plane are plotted. We show that the evolutionary trajectories are dependent on the model parameters of new HDE model. Eventually, in the light of SNe+…
Motivated by recent results on non-vanishing spatial curvature \cite{curve} we employ the holographic model of dark energy to investigate the validity of first and second laws of thermodynamics in non-flat (closed) universe enclosed by apparent horizon $R_A$ and the event horizon measured from the sphere of horizon named $L$. We show that for the apparent horizon the first law is roughly respected for different epochs while the second laws of thermodynamics is respected while for $L$ as the system's IR cut-off first law is broken down and second law is respected for special range of decelerati…
The braneworld model proposed by Dvali, Gabadadze and Porrati leads to an accelerated universe without cosmological constant or other form of dark energy. Nevertheless, we have investigated the consequences of this model when an holo- graphic dark energy is included, taken the Hubble scale as IR cutoff. We have found that the holographic dark energy leads to an accelerated universe flat (de Sitter like expansion) for the two branch: {\ko} = \pm1 of the DGP model. Nevertheless, in universes with no null curvature the dark energy presents an EoS corresponding to a phantom fluid during the presen…
In this paper, we have examined the R$\acute{e}$nyi holographic dark energy (RHDE) model in the framework of an isotropic and spatially homogeneous flat FLRW (Friedmann- Lema$\hat i$tre-Robertson-Walker) Universe by considering different values of parameter $δ$, where the infrared cut-off is taken care by the Hubble horizon. We examined the RHDE model through the analysis of the growth rate of perturbations and the statefinder hierarchy. The evolutionary trajectories of the statefinder hierarchy $S_3^1$, $S_3^2$ $S_4^1$, $S_4^2$ versus redshift $z$, shows satisfactory behaviour throughout the …
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. It is also concluded that if the universe continues to expand, then one day it might be completely filled with dark energy.
In this work, we consider homogeneous and isotropic FRW model of the universe, filled with interacting dark matter and dark energy. The dark matter is chosen as usual in the form of dust while dark energy is holographic in nature with IR cut off at the Ricci's length and it is in the form of a perfect fluid with variable equation of state. We have chosen the interaction term of the following two types: (i) a linear combination of the matter density of the two fluids, (ii) a product of the two matter densities. For both the choices the evolution equations are transformed to an autonomous system…
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 paper, we study the interacting DGP braneworld Holographic Dark Energy model in a spatially flat FRW universe. Mainly, in this study we concentrate our attention on both interacting and non-interacting form of the model. The study shows that the equation of state and the deceleration parameter depict an accelerated universe for all variety of interactions. On the other hand, the StateFinder analysis shows that of the interacting and non-interacting behave similar to both quintessence and phantom dark energy and for the present value obey the behavior of quintessence. Moreover, the resu…
In the present work, we investigate the power-law entropy corrected holographic dark energy (PLECHDE) model with Hubble horizon cutoff. We use 46 observational Hubble data points in the redshift range $0 \leq z \leq 2.36$ to determine the present Hubble constant $H_0$ and the model parameter $n$. It represents a phase transition of the universe from deceleration to acceleration and has the transition point at $z_t = 0.71165$. We investigate the observational constraints on the model and calculate some relevant cosmological parameters. We examine the model's validity by drawing state-finder par…
\begin{abstract} The accelerated expansion of the universe can be interpreted as a tendency to satisfy the holographic equipartition. It can be expressed by a simple law, $ΔV = Δt\left(N_{surf}-εN_{bulk}\right),$ where $V$ is the Hubble volume in Plank units, $t$ is the cosmic time plank units and $N_{surf/bulk}$ is the degrees of freedom on the horizon/bulk of the universe. We show that this holographic equipartition law effectively implies the maximization of entropy. In the cosmological context, a system that obeys the holographic equipartition law behaves as an ordinary macroscopic system …
We study the evolution of the universe by assuming an integrated model, which involves interacting dark energy and holographic principle with Hubble scale as IR cutoff. First we determined the interaction rate at which matter is converting to dark energy. In the next step, we evaluated the equation of state parameter which describes the nature of dark energy. Our result predicts that the present state of the universe is dominated by quintessence type dark energy and it will become phantom dominated in near future. Again our analysis successfully addresses the problem of present accelerated exp…
