Holographic Dark Energy in Higher Derivative Gravity with Varying Gravitational Constant

In this paper we investigate the holographic dark energy scenario in higher derivative gravity with a varying gravitational constant. We introduce a kind of energy density from higher derivative gravity which has role of the same as holographic dark energy. We obtain the exact differential equation , which determine the evolution of the dark energy density based on varying gravitational constant G. We also find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for low redshifts containing varying G correction.     

Holographic dark energy with varying gravitational constant

We investigate the holographic dark energy scenario with a varying gravitational constant, in flat and non-flat background geometry. We extract the exact differential equations determining the evolution of the dark energy density-parameter, which include G-variation correction terms. Performing a low-redshift expansion of the dark energy equation of state, we provide the involved parameters as functions of the current density parameters, of the holographic dark energy constant and of the G-variation.     

A Note on Holographic Dark Energy with Varying <Emphasis Type="Italic">c</Emphasis><Superscript>2</Superscript> Term

We reconsider the holographic dark energy (HDE) model with a slowly time varying c ²(z) parameter in the energy density, namely \(\rho _{D}=3{M_{p}^{2}} c^{2}(z)/L^{2}\), where L is the IR cutoff and z is the redshift parameter. As the system’s IR cutoff we choose the Hubble radius and the Granda-Oliveros (GO) cutoffs. The latter inspired by the Ricci scalar curvature. We derive the evolution of the cosmological parameters such as the equation of state and the deceleration parameters as the explicit functions of the redshift parameter z. Then, we plot the evolutions of these cosmological parameters in terms of the redshift parameter during the history of the universe. Interestingly enough, we observe that by choosing L = H ^?1 as the IR cutoff for the HDE with time varying c ²(z) term, the present acceleration of the universe expansion can be achieved, even in the absence of interaction between dark energy and dark matter. This is in contrast to the usual HDE model with constant c ² term, which leads to a wrong equation of state, namely that for dust w _D =0, when the IR cutoff is chosen the Hubble radius.     

Modified holographic dark energy in non-flat Kaluza–Klein universe with varying <Emphasis Type="Italic">G</Emphasis>

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 ΛCDM model.     

Holographic Ricci Dark Energy Model with Non-constant c 2 Term

In this paper, we study holographic Ricci dark energy model with non-constant c ² term in dark energy density formula. We consider FRW metric in flat space-time and calculate density. Also we find scale factor and Hubble expansion parameter.     

Holographic dark energy in Brans–Dicke cosmology with chameleon scalar field

We study a cosmological implication of holographic dark energy in the Brans–Dicke gravity. We employ the holographic model of dark energy to obtain the equation of state for the holographic energy density in non-flat (closed) universe enclosed by the event horizon measured from the sphere of horizon named L. Our analysis shows that one can obtain the phantom crossing scenario if the model parameter α (of order unity) is tuned accordingly. Moreover, this behavior is achieved by treating the Brans–Dicke scalar field as a Chameleon scalar field and taking a non-minimal coupling of the scalar field with matter. Hence one can generate phantom-like equation of state from a holographic dark energy model in non-flat universe in the Brans–Dicke cosmology framework.     

Possible theoretical limits on holographic quintessence from weak gravity conjecture

The holographic dark energy model is one of the important ways for dealing with the dark energy problems in the quantum gravity framework. In this model, the dimensionless parameter c   plays an essential role in determining the evolution of the holographic dark energy. In particular, the holographic dark energy with c?1$c?1$ can be effectively described by a quintessence scalar-field. However, according to the requirement of the weak gravity conjecture the variation of the quintessence scalar-field should be less than the Planck mass, which would give theoretic constraints on the parameters c   and Ω_m0${\Omega }_{\mathrm{m}0}$. Therefore, we get the possible theoretical limits on the parameter c for the holographic quintessence model.     

Kaluza–Klein cosmology with modified holographic dark energy

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.     

Power-Law Entropy-Corrected HDE and NADE in Brans-Dicke Cosmology

Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields inside and outside the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relevant cosmological parameters and their evolution. As a result we find that this model can provide the present cosmic acceleration and even the equation of state parameter of this model can cross the phantom line w _D =−1 provided the model parameters are chosen suitably.     

A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity

This paper is devoted to study some holographic dark energy models in the context of Chern-Simon modified gravity by considering FRW universe. We analyze the equation of state parameter using Granda and Oliveros infrared cut-off proposal which describes the accelerated expansion of the universe under the restrictions on the parameter α. It is shown that for the accelerated expansion phase \( -1<\omega _{\Lambda }<-\frac {1}{3}\), the parameter α varies according as \(1<\alpha <\frac {3}{2}\). Furthermore, for 0<α<1, the holographic energy and pressure density illustrates phantom-like theory of the evolution when ω_Λ<?1. Also, we discuss the correspondence between the quintessence, K-essence, tachyon and dilaton field models and holographic dark energy models on similar fashion. To discuss the accelerated expansion of the universe, we explore the potential and the dynamics of quintessence, K-essence, tachyon and dilaton field models.     

Interacting New Agegraphic Viscous Dark Energy with Varying <Emphasis Type="Italic">G</Emphasis>

We consider the new agegraphic model of dark energy with a varying gravitational constant, G, in a non-flat universe. We obtain the equation of state and the deceleration parameters for both interacting and noninteracting new agegraphic dark energy. We also present the equation of motion determining the evolution behavior of the dark energy density with a time variable gravitational constant. Finally, we generalize our study to the case of viscous new agegraphic dark energy in the presence of an interaction term between both dark components.     

Interacting ghost dark energy in Brans-Dicke theory

We investigate the QCD ghost model of dark energy in the framework of Brans-Dicke cosmology. First, we study the non-interacting ghost dark energy in a flat Brans-Dicke theory. In this case we obtain the equation of state and the deceleration parameters and a differential equation governing the evolution of ghost energy density. Interestingly enough, we find that the equation of state parameter of the non-interacting ghost dark energy can cross the phantom line (wD=−1) provided the parameters of the model are chosen suitably. Then, we generalize the study to the interacting ghost dark energy in both flat and non-flat Brans-Dicke framework and find out that the transition of wD to phantom regime can be more easily achieved for than when resort to the Einstein field equations is made.     

Holographic Ricci dark energy in Randall–Sundrum braneworld: Avoidance of big rip and steady state future

In the holographic Ricci dark energy (RDE) model, the parameter α plays an important role in determining the evolutionary behavior of the dark energy. When α<1/2, the RDE will exhibit a quintom feature, i.e., the equation of state of dark energy will evolve across the cosmological constant boundary w=−1. Observations show that the parameter α is indeed smaller than 1/2, so the late-time evolution of RDE will be really like a phantom energy. Therefore, it seems that the big rip is inevitable in this model. On the other hand, the big rip is actually inconsistent with the theoretical framework of the holographic model of dark energy. To avoid the big rip, we appeal to the extra dimension physics. In this Letter, we investigate the cosmological evolution of the RDE in the braneworld cosmology. It is of interest to find that for the far future evolution of RDE in a Randall–Sundrum braneworld, there is an attractor solution where the steady state (de Sitter) finale occurs, in stead of the big rip.     

Evolution of Holographic Dark Energy in Interacting Modified Chaplygin Gas Model

We investigate the modified Chaplygin gas （MCG） with interaction between holographic dark energy proposed by Li and dark matter. In this model, evolution of the universe is described in detail, which is from deceleration to acceleration. Specifically, the evolutions of related cosmological quantities such as density parameter, the equation of state of holographic dark energy, deceleration parameter and transition redshift are discussed. Moreover, we also give their present values which are consistent with the lately observations. Furthermore, the results given by us show such a model can accommodate a transition of the dark energy from a normal state wx 〉 -1 to ωx 〈 -1 phantom regimes.     

Variable <Emphasis Type="Italic">G</Emphasis> Corrections to Statefinder Parameters of Dark Energy

Motivated by several observational and theoretical developments concerning the variability of Newton’s gravitational constant with time G(t), we calculate the varying G correction to the statefinder parameters for four models of dark energy namely interacting dark energy holographic dark energy, new-agegraphic dark energy and generalized Chaplygin gas.     

Diagnosing ΛHDE model with statefinder hierarchy and fractional growth parameter

Recently, a new dark energy model called ΛHDE was proposed. In this model, dark energy consists of two parts: cosmological constant Λ and holographic dark energy(HDE). Two key parameters of this model are the fractional density of cosmological constant ?_(Λ0), and the dimensionless HDE parameter c. Since these two parameters determine the dynamical properties of DE and the destiny of universe, it is important to study the impacts of different values of ?_(Λ0) and c on the ΛHDE model. In this paper,we apply various DE diagnostic tools to diagnose ΛHDE models with different values of ?_(Λ0) and c; these tools include statefinder hierarchy{S_3~(1), S_4~(1)}, fractional growth parameter ?, and composite null diagnostic(CND), which is a combination of{S_3~(1), S_4~(1)}and ?. We find that:(1) adopting different values of ?_(Λ0) only has quantitative impacts on the evolution of the ΛHDE model, while adopting different c has qualitative impacts;(2) compared with S_3~(1), S_4~(1) can give larger differences among the cosmic evolutions of the ΛHDE model associated with different ?_(Λ0) or different c;(3) compared with the case of using a single diagnostic, adopting a CND pair has much stronger ability to diagnose the ΛHDE model.     

Interacting generalized ghost dark energy in a non-flat universe

We investigate the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity. First, we study the non-interacting generalized ghost dark energy in a flat Friedmann-Robertson-Walker (FRW) background. We obtain the equation of state parameter, w _D = p/ρ, the deceleration parameter, and the evolution equation of the generalized ghost dark energy. We find that, in this case, w _D cannot cross the phantom line (w _D > ?1) and eventually the universe approaches a de-Sitter phase of expansion (w _D → ?1). Then, we extend the study to the interacting ghost dark energy in both a flat and non-flat FRW universe. We find that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (w _D < ?1) provided the parameters of the model are chosen suitably. Finally, we constrain the model parameters by using the Markov Chain Monte Carlo (MCMC) method and a combined dataset of SNIa, CMB, BAO and X-ray gas mass fraction.     

Statefinder Parameters for Different Dark Energy Models with Variable G Correction in Kaluza-Klein Cosmology

In this work, we have calculated the deceleration parameter, statefinder parameters and EoS parameters for different dark energy models with variable G correction in homogeneous, isotropic and non-flat universe for Kaluza-Klein Cosmology. The statefinder parameters have been obtained in terms of some observable parameters like dimensionless density parameter, EoS parameter and Hubble parameter for holographic dark energy, new agegraphic dark energy and generalized Chaplygin gas models.     

Interacting holographic dark energy in Brans–Dicke theory

We study cosmological application of interacting holographic energy density in the framework of Brans–Dicke cosmology. We obtain the equation of state and the deceleration parameter of the holographic dark energy in a non-flat universe. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as L=ar(t)$L=ar(t)$. We find that the combination of Brans–Dicke field and holographic dark energy can accommodate wD=−1$w_D=-1$ crossing for the equation of state of noninteracting   holographic dark energy. When an interaction between dark energy and dark matter is taken into account, the transition of wD$w_D$ to phantom regime can be more easily accounted for than when resort to the Einstein field equations is made.