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.
We construct a DGP-inspired braneworld model where induced gravity on the brane is modified in the spirit of $f(R)$ gravity and stringy effects are taken into account by incorporation of the Gauss-Bonnet term in the bulk action. We explore cosmological dynamics of this model and we show that this scenario is a successful alternative for dark energy proposal. Interestingly, it realizes the phantom-like behavior without introduction of any phantom field on the brane and the effective equation of state parameter crosses the cosmological constant line naturally in the same way as observational dat…
In this thesis we investigate certain cosmological brane world models of the Randall-Sundrum type. The models are motivated by string theory but we focus on the phenomenology of the cosmology. Two models of specific interest are the Dvali-Gabadadze-Porrati (DGP, induced-gravity) model, where the brane action is modified, and the Gauss-Bonnet model where the bulk action is modified. Both of these modifications maybe motivated by string theory. We provide a brief review of Randall-Sundrum models and then consider the Kaluza-Klein modes on Minkowski and de Sitter branes, in both the two and one b…
The DGP brane world model allows us to get the observed late time acceleration via modified gravity, without the need for a ``dark energy'' field. This can then be generalised by the inclusion of high energy terms, in the form of a Gauss-Bonnet bulk. This is the basis of the Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and late time modifications to the cosmological evolution. Recently the simplest GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of the three possible branches in these models start with a finite density ``Big-Bang'' and with …
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 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.
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.
In this letter, we have considered that the universe is filled with normal matter and variable modified Chaplygin gas. Also we have considered the interaction between normal matter and variable modified Chaplygin gas in FRW universe. Then we have considered a correspondence between the holographic dark energy density and interacting variable modified Chaplygin gas energy density. Then we have reconstructed the potential of the scalar field which describes the variable modified Chaplygin cosmology.
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.
A reconstruction of modified gravity is proposed by establishing a correspondence between the effective density of the modified gravity and the holographic density. The non-homogeneous term in the modified Friedmann equation, generated by the vacuum (holographic) energy density, lead to reconstructed models that contain explicitly, as part of the solution, the Einstein-Hilbert term. It was shown that the $Λ$CDM-type cosmic histories allow the general relativity Lagrangian with cosmological constant as a particular reconstructed solution. The Starobinsky term appears in some reconstructed solut…
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.
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.
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…
Here, we peruse cosmological usage of the most promising candidates of dark energy in the framework of f(R) theory. We reconstruct the different f(R) modified gravity models in the spatially flat FRW universe according to the ordinary and entropy-corrected versions of the holographic and new agegraphic dark energy models, which describe accelerated expansion of the universe. We also obtain the equation of state parameter of the corresponding f(R)-gravity models. We conclude that the holographic and new agegraphic f(R)-gravity models can behave like phantom or quintessence models. Whereas the e…
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<ω_Λ<-\frac{1}{3}$, the parameter $α$ varies according as $1<α<\frac{3}{2}$. Furthermore, for $0<α<1$, the holographic energy and pressure density illustrates phantom-like theory of the evolution when $…
We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it's found that the second law can be …
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 study the effects which are produced by the interaction between a brane Universe and the bulk in which the Universe is embedded. Taking into account the effects produced by the interaction between a brane Universe and the bulk, we derived the Equation of State (EoS) parameter $ω_D$ for three different models of Dark Energy (DE), \emph{i.e.} the Holographic DE (HDE) model with infrared (IR) cut-off given by the Granda-Oliveros cut-off, the Modified Holographic Ricci DE (MHRDE) model and a DE model which is function of the Hubble parameter $H$ squared and to higher derivatives …
We discuss the recently suggested Ricci-Gauss-Bonnet holographic dark energy in Chern-Simons modified gravity. We have tested some general forms of the scale factor $a(t)$, and used two physically reasonable forms which have been proved to be consistent with observations. Both solutions predict a sign flipping in the evolution of cosmic pressure which is positive during the early-time deceleration and negative during the late-time acceleration. This sign flipping in the evolution of cosmic pressure helps in explaining the cosmic deceleration-acceleration transition, and it has appeared in othe…
We explore the cosmological aspects of interacting Tsallis holographic dark energy (THDE) in a $q$-modified DGP braneworld setup emerging from non-Gaussian statistical mechanics.To this end, three classes of superstatistics, that is, log-normal, inverse $χ^2$ and $χ^2$ superstatistics were incorporated into the model. We examined the implication of the three superstatistics on different cosmological parameters, namely, the dimensionless energy density and the equation-of-state (EoS) of THDE, along with the deceleration parameter and the squared speed of sound. As a result, we noted that the co…
We define a "holographic limit" of Lancsoz-Lovelock theories at the Lagrangian level which gives three-dimensional modified gravity theories. We also show that this limit applies to more general classes of theories in higher dimensions provided that they admit the holographic c-theorem.
We show that field equations of some typical modified gravity theories can be recast as thermodynamic first law on dynamical holographic screens. The thermodynamic second law are also presented.
In this paper, we investigate the validity of the generalized second law of thermodynamics of the universe bounded by the event horizon. Here we consider homogeneous and isotropic model of the universe filled with perfect fluid in one case and in another case holographic model of the universe has been considered. In the third case the matter in the universe is taken in the form of non-interacting two fluid system as holographic dark energy and dust. Here we study the above cases in the Modified gravity, f(R) gravity.
We study non-viscous and viscous holographic dark energy models for a homogeneous and isotropic flat Friedmann-Robertson-Walker Universe in $f(R,T)$ gravity. We find that the Hubble horizon as an IR cut-off is suitable for both the models to explain the recent accelerated expansion of the Universe. The cosmological parameters like deceleration parameter and statefinder parameters are discussed in each model. In non-viscous model a constant deceleration parameter is found which shows that there is no phase transition. The constraints on the parameters are obtained to analyse the fixed point val…
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.
The application of holographic principle in very early time is studied. The consideration of the principle in the late-time evolution will be a good motivation to study its role at the time of inflation. Since the length scale is expected to be small during inflation, the resulted energy density form the holographic principle is expected to be large enough to drive inflation. The entropy of the system is the main part of the holographic principle, in which modifying entropy will leads to a modified energy density. Here, instead of the original entropy, we are going to apply a modified entropy,…
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 have investigated the physical behavior of cosmological models in the framework of modified Teleparallel gravity. This model is established using a Renyi holographic ``dark energy model (RHDE) with a Hubble cutoff. Here we have considered a homogeneous and isotropic Friedman universe filled with perfect `fluid. The physical parameters are derived for the present model in Compliances with 43 observational Hubble data sets (OHD). The equation of state (EoS) parameter in terms of $H(z)$ describes a the transition of the universe between phantom and non-phantom phases in the cont…
In the present work, we reconstruct different f(T)-gravity models corresponding to the original and entropy-corrected version of the holographic and new agegraphic dark energy models. We also obtain the equation of state parameters of the corresponding f(T)-gravity models. We conclude that the holographic and new agegraphic f(T)-gravity models behave like phantom or quintessence model. Whereas in the entropy-corrected models, the equation of state parameter can justify the transition from the quintessence state to the phantom regime as indicated by the recent observations.
In this paper, bulk viscosity is introduced in new holographic dark energy (HDE) to describe the effects of cosmic non-perfect fluid on the evolution of the universe in modified $f(R,T)$ gravity. Assuming $f(R,T)=R+λT$, where $R$ is the Ricci scalar, $T$, the trace of energy-momentum tensor and $λ$ is a constant, we derive a general function of Hubble parameter with bulk viscous form to provide a procedure for the viscous new HDE model building. Especially, we assume the total bulk viscosity coefficient proportional to the velocity of the expansion of the universe in such a way that $ζ=ζ_0+ζ_1…
We studied a unified approach with the holographic, new agegraphic and the $f(R)$ dark energy model to construct the form of $f(R)$ which in general responsible for the curvature driven explanation of the very early inflation along with presently observed late time acceleration. We considered the generalized uncertainty principle in our approach which incorporated the corrections in the entropy area relation and thereby modified the energy densities for the cosmological dark energy models considered. We found that holographic and new agegraphic $f(R)$ gravity models can behave like phantom or …
We make a scalar representation of interactive models with cold dark matter and modified holographic Ricci dark energy through unified models driven by scalar fields with non-canonical kinetic term. These models are applications of the formalism of exotic k-essences generated by the global description of cosmological models with two interactive fluids in the dark sector and in these cases they correspond to usual k-essences. The formalism is applied to the cases of constant potential in Friedmann-Robertson-Walker geometries.
Employing a thermodynamic interpretation of gravity based on the holographic principle and assuming underlying particle statistics, fermionic or bosonic, for the excitations of the holographic screen leads to Modified Newtonian Dynamics (MOND). A connection between the acceleration scale $a_0$ appearing in MOND and the Fermi energy of the holographic fermionic degrees of freedom is obtained. In this formulation the physics of MOND results from the quantum-classical crossover in the fermionic specific heat. However, due to the dimensionality of the screen, the formalism is general and applies t…
In this paper, the cosmological dynamics of a modified holographic dark energy which is derived from the UV/IR duality by considering the black hole mass in higher dimensions as UV cutoff, is investigated in Dvali-Gabadaze-Porrati (DGP) brane world model. We choose Hubble horizon and future event horizon as IR cutoff respectively. And the two branches of the DGP model are both taken into account. When Hubble horizon is considered as IR cutoff, the modified holographic dark energy (HDE) behaves like an effect dark energy that modification of gravity in pure DGP brane world model acts and it can…
This paper is devoted to study the modified holographic dark energy model by taking its different aspects in the flat Kaluza-Klein universe. We construct the equation of state parameter which evolutes the universe from quintessence region towards the vacuum. It is found that the modified holographic model exhibits instability against small perturbations in the early epoch of the universe but becomes stable in the later times. We also develop its correspondence with some scalar field dark energy models. It is interesting to mention here that all the results are consistent with the present obser…
We considered the Tsallis holographic dark energy model in frames of Nojiri-Odintsov gravity with $f(R)=R+λR^2-σμ/{R}$. For IR cutoff event horizon is taken. The cosmological evolution of such universe is investigated for various initial conditions and values of parameters. The dependence of the Hubble parameter $H$ from time in the future has an oscillations. It is shown that for $μ\neq 0$ appearance of singularities are typical and the time up to these singularities can be relatively small from cosmological viewpoint. The singularity is associated with the zero of second deribative of $f(R)$…
Verlinde has suggested that the gravity has an entropic origin, and a gravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature $T_D$. The modified entropic force returns to the Newton's law of gravitation whi…
A new conception is proposed in Ref.\cite{Verlinde:2010hp,Padmanabhan:2009kr} that gravity is one kind of entropic force. In this letter, we try to discuss its applications to the modified gravities by using three different corrections to the area law of entropy which are derived from the quantum effects and extra dimensions. According to the assumption of holographic principle, the number of bits $N$ which is related to the equipartition law of energy is modified. Then, the modified law of Newton's gravity and the modified Friedmann equations are obtained by using the new notion. By choosing …
We show that in the standard derivation of the holographic dark energy some conceptual issues are present. In particular, the formula used in the literature to avoid black holes is not suitable in expanding universes. A more suitable expression for a holographic motivated dark energy must contain the energy density of the remaining matter content of the universe. However, we show that under some reasonable hypothesis, we can obtain a new physically motivated expression for the holographic dark energy. By considering an appropriate time-dependence of the saturation-level parameter, a de Sitter …
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…
In the emergent cosmic space scenario recently proposed by Padmanabhan, the expansion of the universe is attributed to the difference between the number of degrees of freedom on a holographic surface and the one in the bulk. Based on this idea, we explore the cases where logarithmic and power-law entropic corrections are present, respectively. The previously found modified Friedmann equations are reproduced through an improved proposal, and we show that the same results can be obtained using a generalized expansion law.
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 evolution of a bound system in the expanding background has been investigated in this paper. The background is described by a FRW universe with the modified holographic dark energy model, whose equation of state parameter changes with time and can cross the phantom boundary. To study the evolution of the bound system, an interpolating metric is considered, and on this basis the geodesics of a test particle are given. The equation of motion and the effective potential are also derived from the geodesics. By studying the the effective potential and the evolution of the radius of a test parti…
We study the entropy-corrected version of the holographic dark energy (HDE) model in the framework of modified FRW cosmology. We consider a non-flat universe filled with an interacting viscous entropy-corrected HDE (ECHDE) with dark matter. We also include the case of variable gravitational constant G in our model. We obtain the equation of state and the deceleration parameters of the interacting viscous ECHDE. Moreover, we reconstruct the potential and the dynamics of the quintessence, tachyon, K-essence and dilaton scalar field models according to the evolutionary behavior of the interacting…
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, motivated by the energy bound suggested by Cohen {\it et al.}, we propose the modified holographic dark energy (MHDE) model. Choosing the IR cut-off $L=R_{\rm CC}$ and considering the parameterizations $n^2=2-λa$, $n^2=2-3λa^2/(1+3a^2)$ and $n^2=2-λa^2/(β+a^2)$, we derive all the physical quantities of the non-saturated MHDE model analytically. We find that the non-saturated MHDE models with the parameterizations $n^2=2-λa$ and $n^2=2-3λa^2/(1+3a^2)$ are single-parameter models in practice. Also, we consider the cosmological constraints on the non-saturated MHDE, and find that it…
In this work, the PLECHDE model with Granda-Oliveros (G-O) IR-cutoff is studied. The evolution of dark energy density, deceleration and EoS parameters are calculated. I demonstrate that under a condition, our universe can accelerate near the phantom barrier at present time. We calculate these parameters also in PLECHDE at Ricci scale, when when $α=2$ and $β=1$, and at last a comparison between Ricci scale, G-O cutoff and non-corrected HDE without matter field with G-O cutoff is done. The correspondence between this model and some scalar field of dark energy models is established. By this metho…
A mapping between two braneworld cosmologies -- Randall-Sundrum and holographic -- is explicitly constructed. The cosmologies are governed by the appropriate modified Friedman equations. A relationship between the corresponding Hubble rates is established.
The modified holographic Ricci dark energy coupled to interacting relativistic and non-relativistic dark matter is considered in the nonflat Friedmann-Robertson-Walker universe. Through examining the deceleration parameter, one can find that the transition time of the Universe from decelerating to accelerating phase in the interacting holographic Ricci dark energy model is close to that in the $Λ$ cold dark matter model. The evolution of modified holographic Ricci dark energy's state parameter and the evolution of dark matter and dark energy's densities shows that the dark energy holds the dom…
In this paper, we reconstruct the holographic dark energy in the framework of $f(G)$ modified theory of gravity, where $G$ is Gauss-Bonnet invariant. In this context, we choose the infrared cut-off as Granda-Oliveros cut-off which is proportional to the Hubble parameter $H$ and its first derivative with respect to the cosmic time $t$. We reconstruct $f(G)$ model with the inclusion of HDE and three well-known forms of the scale factor $a(t)$, i.e. the emergent, the logamediate and the intermediate scale factors. The reconstructed model as well as equation of state parameter are discussed numeri…
In this paper, we derive the Einstein's field equation (EFE) by considering an non-commuting two dimensional quantized space, which can be excited by absorbing energy. Any variation of the energy level of space quantas, will result in a change in the quanta's area state. This means, that the geometry of space depends on the energy which exists in it. Using Holographic principle and Unruh effect, without any further assumptions like equipartition theorem, our model leads to Newton's law of gravity in the limit $\hbar \to 0$.
We investigate a model of interacting dark matter and dark energy given by a modified holographic Ricci cutoff in a spatially flat Friedmann-Robertson-Walker (FRW) space-time. We consider a nonlinear interaction consisting of a significant rational function of the total energy density and its first derivative homogeneous of degree one and show that the effective one-fluid obeys the equation of state of a relaxed Chaplygin gas. So that, the universe is dominated by pressureless dark matter at early times and undergoes an accelerated expansion in the far future driven by a strong negative pressu…
