The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called ``entropy-corrected holographic dark energy'' (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called ``entropy-corrected agegraphic dark energy'' (ECADE).
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…
In this paper, we have considered a cosmological model with the non--minimal kinetic coupling terms and investigated its cosmological implications with respect to the logarithmic entropy-- corrected holographic dark energy (LECHDE). The correspondence between LECHDE in flat FRW cosmology and the phantom dark energy model with the aim to interpret the current universe acceleration is also examined.
In this paper, we have considered $F(R,T)$ gravity as a linear function of the curvature and torsion scalars and interacted it with logarithmic entropy corrected holographic dark energy to evaluate cosmology solutions. The model has been investigated by FRW metric, and then the energy density and the pressure of dark energy have calculated. Also we obtained equation of state (EoS) parameter of dark energy and has plotted it with respect to both variable of cosmic time and $e$-folding number. Finally, we have described the scenario in three status: early, late and future time by $e$-folding num…
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 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 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…
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…
Motivated by the recent works of us [1], we establish a correspondence between f(R)-gravity with the power-law entropy corrected holographic dark energy (PLECHDE) and new agegraphic dark energy (PLECNADE) models. We reconstruct corresponding f(R)-gravities and obtain the equation of state parameters. We show that the selected f(R)-gravity models can accommodate the transition from the quintessence state to the phantom regime as indicated by the recent observations.
We have discussed the correspondence of the well-accepted $f(G)$ gravity theory with two dark energy models : $(m,n)$-type holographic dark energy [$(m,n)$-type HDE] and entropy-corrected $(m,n)$-type holographic dark energy. For this purpose, we have considered the power law form of the scale factor $a(t)=a_{0}t^{p}, p>1$. The reconstructed $f(G)$ in these models have been found and the models in both cases are found to be realistic. We have also discussed the classical stability issues in both models. The $(m,n)$-type HDE and its entropy-corrected versions are more stable than the ordinary H…
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…
In the present work we investigate the cosmological implications of the entropy-corrected holographic dark energy (ECHDE) density in the Gauss-Bonnet framework. This is motivated from the loop quantum gravity corrections to the entropy-area law. Assuming the two cosmological scenarios are valid simultaneously, we show that there is a correspondence between the ECHDE scenario in flat universe and the phantom dark energy model in the framework of Gauss-Bonnet theory with a potential. This correspondence leads consistently to an accelerating universe.
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…
We introduce a new interpretation of chemical potential and show that holographic entropy is entropy bound, which is supported by two ideal cases discussed in detail. One is sparse but incompressible liquid like a star of uniform density and the other is a screen at infinity in spherically symmetric sapcetime. Our work is based on the new scenario of entropy force and holographic thermodynamics, and the Brown-York quasi-local energy.
By considering the logarithmic correction to the energy density, we study the behavior of Hubble parameter in the holographic dark energy model. We assume that the universe is dominated by interacting dark energy and matter and the accelerated expansion of the universe, which may be occurred in the early universe or late time, is studied.
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…
A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the $α$-th power of the Hubble parameter, where $α$ is a dimensionless constant for the power-law c…
Here, we peruse cosmological usage of the most promising candidates of dark energy in the framework of $f(T)$ gravity theory. We reconstruct the different $f(T)$ modifed gravity models in the spatially flat FRW universe according to entropy-corrected versions of the holographic and new agegraphic dark energy models in power-law and logarithmic corrections, which describe accelerated expansion history of the universe. We conclude that the equation of state parameter of the entropy-corrected models can transit from quintessence state to phantom regime as indicated by recent observations or can l…
Here we briefly discuss the Einstein-Aether gravity theory by modification of Einstein-Hilbert action. We find the modified Friedmann equations and then from the equations we find the effective density and pressure for Einstein-Aether gravity sector. These can be treated as dark energy provided some restrictions on the free function $F(K)$, where $K$ is proportional to $H^{2}$. Assuming two types of the power law solutions of the scale factor, we have reconstructed the unknown function $F(K)$ from HDE and NADE and their entropy-corrected versions (ECHDE and ECNADE). We also obtain the EoS para…
We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.
In this paper, we study the Power Law Entropy Corrected Holographic Dark Energy (PLECHDE) model in the framework of a non-flat Universe and of Hořava-Lifshitz cosmology with infrared cut-off given by recently proposed Granda-Oliveros cut-off, which contains one term proportional to the Hubble parameter squared $H^2$ and one term proportional to the first time derivative of the Hubble parameter $\dot{H}$. Moreover, this cut-off is characterized by two constant parameters, $α$ and $β$. For the two cases corresponding to non-interacting and interacting DE and Dark Matter (DM), we derive the evolu…
We examine the deSitter entropy in the braneworld model with the Gauss-Bonnet/Lovelock terms. Then, we can see that the deSitter entropy computed through the Euclidean action exactly coincides with the holographic entanglement entropy.
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 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…
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…
In this paper, we consider dyonic charged AdS black hole which is holographic dual of a van der Waals fluid. We use logarithmic corrected entropy and study thermodynamics of the black hole and show that holographic picture is still valid. Critical behaviors and stability also discussed. Logarithmic corrections arises due to thermal fluctuations which are important when size of black hole be small. So, thermal fluctuations interpreted as quantum effect. It means that we can see quantum effect of a black hole which is a gravitational system.
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non stationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a Second La…
Using the corrected expression of Hawking temperature derived from the tunneling formalism beyond semiclassical approximation developed by \emph{Banerjee} and \emph{Majhi}\cite{beyond}, we calculate the corrected entropy of a high dimensional Schwarzschild black hole and a 5-dimensional Gauss-Bonnet (GB) black hole. It is shown that the corrected entropy for this two kinds of black hole are in agreement with the corrected entropy formula (\ref{entropy of apparent horiozn}) that derived from tunneling method for a $(n+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe\cite{FRW}. This fea…
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…
In this paper, we analyze the holographic covariant entanglement entropy in the double Wick rotated version of a rotating BTZ black hole (3 dimensional Kerr-AdS solution), where the periodicity of Euclidean time and spatial direction are changed. The dual field theory has negative energy in the Lorentzian signature. The holographic entanglement entropy agrees with its CFT counterpart, which is obtained by a conformal transformation of the correlation functions of twisted operators.
We investigate the behaviors of holographic entanglement entropy for AdS soliton geometries in the presence of higher derivative corrections. We calculate the leading higher derivative corrections for the AdS5 setup in type IIB string and for the AdS4,7 ones in M-theory. We also study the holographic entanglement entropy in Gauss-Bonnet gravity and study how the confinement/deconfinement phase transition observed in AdS solitons is affected by the higher derivative corrections.
Holographic superconductor is an important arena for holography, as it allows concrete calculations to further understand the dictionary between bulk physics and boundary physics. An important quantity of recent interest is the holographic complexity. Conflicting claims had been made in the literature concerning the behavior of holographic complexity during phase transition. We clarify this issue by performing a numerical study on one-dimensional holographic superconductor. Our investigation shows that holographic complexity does not behave in the same way as holographic entanglement entropy. …
From the viewpoint of local quantum field theory, this letter investigates the high-order corrections to the holographic entropy bound. As a result, the logarithmic correction term appears naturally with the definite coefficient $-{1/2}$, which thus provides another semi-classical platform to examine such candidates for quantum gravity as Loop Quantum Gravity and String Theory.
We introduce a simple geometrical construction similar to covariant holographic entanglement entropy but with the addition of a new term proportional to boundary region volume. This new procedure has properties strongly resembling classical Shannon entropy of probability distributions rather than von Neumann entropy, so we call the quantity holographic Shannon entropy. The holographic Shannon entropy of a region $A$ is divergent in AdS/CFT, but upon regulation, it appears to be equal to the outer entropy of the entanglement wedge of $A$ with the entanglement wedge of the complement of $A$ held…
We determine holographically 2-point correlators of gauge invariant operators with large conformal weights and entanglement entropy of strips for a time-dependent anisotropic 5-dimensional asymptotically anti-de Sitter spacetime. At the early stage of evolution where geodesics and extremal surfaces can extend beyond the apparent horizon all observables vary substantially from their thermal value, but thermalize rapidly. At late times we recover quasi-normal ringing of correlators and holographic entanglement entropy around their thermal values, as expected on general grounds. We check the beha…
We propose a new entropy construct that generalizes the Tsallis, Rényi, Sharma-Mittal, Barrow, Kaniadakis, and Loop Quantum Gravity entropies and reduces to the Bekenstein-Hawking entropy in a certain limit. This proposal is applied to the Schwarzschild black hole and to spatially homogeneous and isotropic cosmology, where it is shown that it can potentially describe inflation and/or holographic dark energy.
When a black hole forms from collapse in a holographic theory, the information in the black hole interior remains encoded in the boundary. We prove that the area of the black hole's apparent horizon is precisely the entropy associated to coarse graining over the information in its interior, subject to knowing the exterior geometry. This is the maximum holographic entanglement entropy that is compatible with all classical measurements conducted outside of the apparent horizon. We identify the boundary dual to this entropy and explain why it obeys a Second Law of Thermodynamics.
The holographic entanglement entropy (HEE) of the minimal geometrical deformation (MGD) procedure and extensions (EMGD), is scrutinized within the membrane paradigm of AdS/CFT. The HEE corrections of the Schwarzschild and Reissner--Nordström solutions, due to a finite fluid brane tension, are then derived and discussed in the context of the MGD and the EMGD.
Using a correspondence between the f(T)-gravity with the power-law entropy corrected version of the holographic dark energy model, we reconstruct the holographic f(T)-gravity model with power-law entropy correction. We fit the model parameters by using the latest observational data including type Ia supernovea, baryon acoustic oscillation, cosmic microwave background, and Hubble parameter data. We also check the viability of our model using a cosmographic analysis approach. Using the best-fit values of the model, we obtain the evolutionary behaviors of the effective torsion equation of state p…
We study the holographic entanglement entropy and mutual information for Lorentz boosted subsystems. In holographic CFTs at zero and finite temperature, we find that the mutual information gets divergent in a universal way when the end points of two subsystems are light-like separated. In Lifshitz and hyperscaling violating geometries dual to non-relativistic theories, we show that the holographic entanglement entropy is not well-defined for Lorentz boosted subsystems in general. This strongly suggests that in non-relativistic theories, we cannot make a real space factorization of the Hilbert …
We investigate a holographic version of Maxwell's equal area law analogous to that for the phase transition in the black hole temperature/black hole entropy plane of a charged AdS black hole. We consider proposed area laws for both the black hole temperature/holographic entanglement entropy plane and the black hole temperature/2-point correlation function plane. Despite recent claims to the contrary, we demonstrate numerically that neither proposal is valid. We argue that there is no physical reason to expect such a construction in these planes.
We derive the Einstein field equations and black hole entropy from the first law of thermodynamics on a holographic time-like screen. Because of the universality of gravity, the stress tensor on the screen must be independent of the details of matter fields, so it should be a pure geometric quantity. For simplicity, we assume that the stress tensor on the screen depends on surface Ricci curvature and extrinsic curvature linearly. Then we prove that the surface stress tensor is just the Brown-York stress tensor plus terms which do not affect the field equations of gravitation and the entropy of…
The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson's formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographi…
A simple derivation of the bound on entropy is given and the holographic principle is discussed. We estimate the number of quantum states inside space region on the base of uncertainty relation. The result is compared with the Bekenstein formula for entropy bound, which was initially derived from the generalized second law of thermodynamics for black holes. The holographic principle states that the entropy inside a region is bounded by the area of the boundary of that region. This principle can be called the kinematical holographic principle. We argue that it can be derived from the dynamical …
A new entropy bound, tighter than the standard holographic bound due to Bekenstein, is derived for spacetimes with non-rotating isolated horizons, from the quantum geometry approach in which the horizon is described by the boundary degrees of freedom of a three dimensional Chern Simons theory.
We study the holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics (ENE) in four and five dimensional spacetimes. We find that the holographic entanglement entropy is powerful tool in studying the properties of the holographic phase transition. For the operator $\langle\mathcal{O}_{+}\rangle$, we observe that the entanglement entropy in 4-dimensional spacetime decreases in metal phase but changes non-monotonously in superconducting phase with the increase of the ENE parameter. Interestingly, the change of the entanglement entropy i…
We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to th…
In this paper we show that in addition to the known minimal surfaces which appear in the literature for computing the entanglement entropy there are other minimal surfaces with non-zero extrinsic curvature. We use the approach of regularization procedure for computing the quadratic and cubic curvature invariants on manifolds with squashed cones. The results can be used to find the leading and universal terms of the holographic entanglement entropy to understand which solution corresponds to the actual minimal surface.
In this paper, we study the thermodynamic quantities of Friedmann-Robertson-Walker (FRW) universe by using the tunneling formalism beyond semiclassical approximation developed by \emph{Banerjee} and \emph{Majhi}\cite{beyond0}. For this we first calculate the corrected Hawking-like temperature on apparent horizon by considering both scalar particle and fermion tunneling. With this corrected Hawking-like temperature, the explicit expressions of the corrected entropy of apparent horizon for various gravity theories including Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, $f(R)$ gravity…
We study the possibility that black hole entropy be identified as entropy of entanglement across the horizon of the vacuum of a quantum field in the presence of the black hole. We argue that a recent proposal for computing entanglement entropy using AdS/CFT holography implies that black hole entropy can be exactly equated with entanglement entropy. The implementation of entanglement entropy in this context solves all the problems (such as cutoff dependence and the species problem) typically associated with this identification.
The aim of the present letter is to find the holographic entanglement entropy (HEE) in 2D holographic superconductors (HSC). Indeed, it is possible to compute the exact form of this entropy due to an advantage of approximate solutions inside normal and superconducting phases with backreactions. By making the UV and IR limits applied to the integrals, an approximate expression for HEE is obtained. In case the software cannot calculate minimal surface integrals analytically, it offers the possibility to proceed with a numerical evaluation of the corresponding terms. We'll understand how the area…
We study the effect of anisotropy on holographic entanglement entropy (HEE) and holographic mutual information (MI) in the Q-lattice model, by exploring the HEE and MI for infinite strips along arbitrary directions. We find that the lattice always enhances the HEE. The MI, however, is enhanced by lattice for large sub-regions; while for small sub-regions, the MI is suppressed by the lattice. We also discuss how these phenomena result from the deformation of geometry caused by Q-lattices.
The holographic bound, $S<=A/4{\ell^2_P}$, asserts that the entropy $S$ of a system is bounded from above by a quarter of the area $A$ of a circumscribing surface measured in Planck areas. This bound is widely regarded as part of the elusive fundamental theory of nature. In fact, the bound is known to be valid for generic weakly gravitating isolated systems in {\it three} spatial dimensions. Nevertheless, the entropy content of a physical system is expected to be an increasing function of the number of spatial dimensions (the more the dimensions, the more ways there are to split up a given amo…
We investigate the holographic entanglement entropy in the Rindler-AdS space-time to obtain an exact solution for the corresponding minimal surface. Moreover, the holographic entanglement entropy of the charged single accelerated AdS Black holes in four dimensions is investigated. We obtain the volume of the codimension one-time slice in the bulk geometry enclosed by the minimal surface for both the RindlerAdS space-time and the charged accelerated AdS Black holes in the bulk. It is shown that the holographic entanglement entropy and the volume enclosed by the minimal hyper-surface in both the…
In this paper we consider the holographic DC and Hall conductivity in Einstein-Maxwell-Dilaton in Gauss-Bonnet gravity with momentum dissipation. We analytically derived the DC conductivity and Hall conductivity from the black horizon data, and found that the conductivities are independent on the Gauss-Bonnet coupling. We also used the entropy function formalism to get the conductivities in terms of the charge of the black hole, even without knowing the explicit black hole solutions.
We investigate the behavior of entanglement entropy across the holographic p-wave superconductor phase transition in an Einstein-Yang-Mills theory with a negative cosmological constant. The holographic entanglement entropy is calculated for a strip geometry at AdS boundary. It is found that the entanglement entropy undergoes a dramatic change as we tune the ratio of the gravitational constant to the Yang-Mills coupling, and that the entanglement entropy does behave as the thermal entropy of the background black holes. That is, the entanglement entropy will show the feature of the second order …
