We formulate Barrow holographic dark energy, by applying the usual holographic principle at a cosmological framework, but using the Barrow entropy instead of the standard Bekenstein-Hawking one. The former is an extended black-hole entropy that arises due to quantum-gravitational effects which deform the black-hole surface by giving it an intricate, fractal form. We extract a simple differential equation for the evolution of the dark energy density parameter, which possesses standard holographic dark energy as a limiting sub-case, and we show that the scenario can describe the universe thermal history, with the sequence of matter and dark energy eras. Additionally, the new Barrow exponent $Δ$ significantly affects the dark energy equation of state, and according to its value it can lead it to lie in the quintessence regime, in the phantom regime, or experience the phantom-divide crossing during the evolution.
We use observational data from Supernovae (SNIa) Pantheon sample, as well as from direct measurements of the Hubble parameter from the cosmic chronometers (CC) sample, in order to extract constraints on the scenario of Barrow holographic dark energy. The latter is a holographic dark energy model based on the recently proposed Barrow entropy, which arises from the modification of the black-hole surface due to quantum-gravitational effects. We first consider the case where the new deformation exponent $Δ$ is the sole model parameter, and we show that although the standard value $Δ=0$, which corr…
We construct Barrow holographic dark energy in the case of non-flat universe. In particular, considering closed and open spatial geometry we extract the differential equations that determine the evolution of the dark-energy density parameter, and we provide the analytical expression for the corresponding dark energy equation-of-state parameter. We show that the scenario can describe the thermal history of the universe, with the sequence of matter and dark energy epochs. Comparing to the flat case, where the phantom regime is obtained for relative large Barrow exponents, the incorporation of po…
A study on the effects of implementing the Granda-Oliveros infrared cutoff in the recently introduced Barrow Holographic Dark Energy model is presented, and its cosmological evolution is investigated. We find how the deformation parameter, $Δ$, affects the values of $H(z)$, and find that from this model it is possible to obtain an accelerated expansion regime of the universe at late times. We also obtain that increasing $Δ$ causes the EoS parameter to transition from quintessence to phantom. In addition, we show that the model can be used to describe the know eras of dominance. Finally, after …
Based on the holographic principle and the Barrow entropy, Barrow holographic dark energy had been proposed. In order to analyze the stability and the evolution of Barrow holographic dark energy, we, in this paper, apply the dynamical analysis and statefinder methods to Barrow holographic dark energy with different IR cutoff and interacting terms. In the case of using Hubble horizon as IR cutoff with the interacting term $Q=\fracλ{H}ρ_{m}ρ_{D}$, we find this model is stable and can be used to describe the whole evolution of the universe when the energy transfers from the pressureless matter to…
The holographic cut-off, in the formalism of generalized holographic dark energy (HDE), is generalized to depend on $L_\mathrm{IR} = L_\mathrm{IR} \left( L_\mathrm{p}, \dot L_\mathrm{p}, \ddot L_\mathrm{p}, \cdots, L_\mathrm{f}, \dot L_\mathrm{f}, \cdots, a\right)$, where $L_\mathrm{p}$ and $L_\mathrm{f}$ are the particle horizon and future horizon respectively, and $a$ is the scale factor of the universe. Based on such formalism, we showed that the Barrow entropic dark energy (DE) model is equivalent to the generalized HDE where the respective holographic cut-off is determined by two ways -- …
Barrow proposed that the area law of the entropy associated with a horizon might receive a "fractal correction" due to quantum gravitational effects -- in place of $S\propto A$, we have instead $S\propto A^{1+δ/2}$, where $0\leqslant δ\leqslant 1$ measures the deviation from the standard area law ($δ=0$). Based on black hole thermodynamics, we argue that the Barrow entropy should run (i.e., energy scale dependent), which is reasonable given that quantum gravitational corrections are expected to be important only in high energy regime. When applied to the Friedmann equation, we demonstrate the …
Hints Beyond $Λ$CDM from Barrow and Tsallis Holographic Dark Energy with GO cutoff
Universidad de Lleida（莱里达大学）；Durban University of Technology（德班理工大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（南非理论与计算科学国家研究所）；Universidad Catòlica del Norte（北天主教学会大学）；Shiraz University（设拉子大学）
In this paper, using Barrow entropy, we propose an interacting model of Barrow holographic dark energy (BHDE). In particular, we study the evolution of a spatially flat FLRW universe composed of pressureless dark matter and BHDE that interact with each other through a well-motivated interaction term. Considering the Hubble horizon as the IR cut-off, we then study the evolutionary history of important cosmological parameters, particularly, the density parameter, the equation of state parameter, and the deceleration parameter in the BHDE model and find satisfactory behaviors in the model. We per…
We present modified cosmological scenarios that arise from the application of the "gravity-thermodynamics" conjecture, using the Barrow entropy instead of the usual Bekenstein-Hawking one. The former is a modification of the black hole entropy due to quantum-gravitational effects that deform the black-hole horizon by giving it an intricate, fractal structure. We extract modified cosmological equations which contain new extra terms that constitute an effective dark-energy sector, and which coincide with the usual Friedmann equations in the case where the new Barrow exponent acquires its Bekenst…
In this work, we have discussed a spatially homogeneous and anisotropic Bianchi type-I space-time in the presence of Barrow holographic dark energy (infrared cut-off is the Hubble's horizon) proposed by Barrow recently (Physics Letters B 808 (2020): 135643) and matter in the framework of $f(Q)$ gravity where the non-metricity $Q$ is responsible for the gravitational interaction for the specific choice of $f(Q)=λQ^{2}$ (where $λ<0$ is a constant). To find the exact solutions to the field equations we consider the deceleration parameter $q$ is a function of the Hubble's parameter $H$ i.e. $q=b-\…
In this work we have investigated the inflation mechanism driven by the Barrow Holographic dark energy (BHDE) in the early universe. BHDE is based on the Barrow relation for horizon entropy, which in turn is inspired from the shape of the COVID-19 virus. It was shown by Barrow that the quantum gravitational effects may instigate complex fractal features in the structure of a black hole. Since the length scale during the inflation is expected to be small, the energy density obtained from the application of the holographic principle in the early universe will be large enough to support the infla…
Recently, Barrow holographic dark energy (BHDE), based on Barrow entropy, has been proposed to describe the late acceleration of the universe. Contrary to the earlier analysis of this model in the literature, we consider the BHDE with the Granda-Oliveros length as IR cut-off, as a dynamical vacuum, having a constant equation of state $ω_Λ=-1.$ We have analytically solved for the Hubble parameter and studied the evolution of cosmological parameters. The model is compared with the observational data on Hubble parameter (OHD36) and Supernovae type Ia (SN Ia), the pantheon data. In the absence of …
The paper presents Barrow holographic dark energy (infrared cut-off is the Hubble horizon) suggested by Barrow recently (Physics Letters B 808 (2020): 135643) in an anisotropic Bianchi type-I Universe within the framework of $% f\left( Q\right) $ symmetric teleparallel gravity, where the non-metricity scalar $Q$ is responsible for the gravitational interaction. We consider two cases: Interacting and non-interacting models of pressureless dark matter and Barrow holographic dark energy by solving $f\left( Q\right) $ symmetric teleparallel field equations. To find the exact solutions of the field…
In this paper, we have used the state finder hierarchy for Barrow holographic dark energy (BHDE) model in the system of the FLRW Universe. We apply two DE diagnostic tools to determine $ΛBHDE$ model to have various estimations of $\triangle$. The first diagnostic tool is the state finder hierarchy in which we have studied $S^{(1)}_{3}$ $S^{(1)}_{4}$, $S^{(2)}_{3}$ $S^{(2)}_{4}$ and second is the composite null diagnostic (CND) in which the trajectories ( $S^{(1)}_{3} - ε$), ($S^{(1)}_{4}-ε$), ($S^{(2)}_{3}-ε$)($S^{(2)}_{4}-ε$) are discussed, where $ε$ is fractional growth parameter. The infrar…
In this work, we propose a new dark energy model by applying the Barrow entropy and the holographic principle, with a time scale as IR cut off. Analysing the conformal time as well as universe's age as infrared cut-offs, we explore the cosmological importance of the suggested dark energy models and examine the universe evolution filled with the proposed DE applicants and a pressure-less matter. We observe that the equation of state, deceleration, the density parameters can present adequate nature, and these models may also explain the late-time acceleration though, the proposed models are unst…
In the present work, we have analyzed the behaviors of extension of generalized Barrow holographic dark energy(`BHDE'). A ``generalized BHDE model based on the particle and the future horizon using infrared cut-off" was proposed by Nojiri et al. (2022). In this work, we have reviewed the generalized BHDE extension under the assumption of a generalized HDE cut-off. Using a scale factor of the form $a = k t^m$, the dynamics of the cosmos have been discussed through graphic demonstration. By applying the ``open-source emcee Python package", the values of the free parameters $k$ and $m$ are estima…
Reconstructions of $f(\mathcal{P})$ and $f(\mathcal{Q})$ gravity models from $(m,n)$-type Barrow Holographic Dark Energy: Analysis and Observational Constraints
We have analyzed the Barrow holographic dark energy (BHDE) in the framework of the flat FLRW Universe by considering the various estimations of Barrow exponent $\triangle$. Here we define BHDE, by applying the usual holographic principle at a cosmological system, for utilizing the Barrow entropy rather than the standard Bekenstein-Hawking. To understand the recent accelerated expansion of the universe, considering the Hubble horizon as the IR cut-off. The cosmological parameters, especially the density parameter ($Ω_{_D}$), the equation of the state parameter ($ω_{_D}$), energy density ($ρ_{_{…
We apply the full set of most update dynamical and geometrical data in cosmology to the nonextensive Barrow entropic holographic dark energy. We show that the data point towards an extensive Gibbs-like entropic behaviour for the cosmological horizons, which is the extreme case of the Barrow entropy, with the entropy parameter being $Δ> 0.86$, close to the maximum threshold of $Δ=1$ where the fractal dimension of the area-horizon becomes almost or just the volume and the intensivity is recovered. Futhermore, we find that the standard Bekenstein area-entropy limit ($Δ= 0$) is excluded by the set…
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.
We investigate the validity of the generalized second law of thermodynamics, applying Barrow entropy for the horizon entropy. The former arises from the fact that the black-hole surface may be deformed due to quantum-gravitational effects, quantified by a new exponent $Δ$. We calculate the entropy time-variation in a universe filled with the matter and dark energy fluids, as well as the corresponding quantity for the apparent horizon. We show that although in the case $Δ=0$, which corresponds to usual entropy, the sum of the entropy enclosed by the apparent horizon plus the entropy of the hori…
Thermodynamic Topology and Photon Spheres Analysis of Black Holes in Brane-World: Insights from Barrow Entropy
Fukushima University（福岛大学）；Zhejiang University of Technology（浙江工业大学）；COMSATS University Islamabad, Lahore-Campus（科姆斯特斯伊斯兰堡大学拉合尔校区）；University of Mazandaran（马赞达兰大学）
Taking into account a fractal structure for the black hole horizon, Barrow argued that the area law of entropy is modified due to quantum-gravitational effects (Barrow in Phys Lett B 808:135643, https://doi.org/10.1016/j.physletb.2020.135643, 2020). Accordingly, the corrected entropy takes the form $S \sim A^{1+\mathrmΔ/2}$, where $0\leq\mathrmΔ\leq1$, indicates the amount of the quantum-gravitational deformation effects. In this paper, based on Barrow entropy, we first derive the modified gravitational field equations through the Clausius relation. We then consider the Friedmann-Lemaître-Robe…
Cosmographic Connection Between Cosmological And Planck Scales: The Barrow-Tsallis Entropy
National Science Center Kharkov Institute of Physics and Technology（哈尔科夫物理与技术国家科学中心）；V. N. Karazin Kharkiv National University（V.N. 卡拉金哈尔科夫国立大学）；Institute for Single Crystals, NAS Ukraine（乌克兰科学院单晶研究所）
In this work we study a non-flat Friedmann-Robertson-Walker universe filled with a pressure-less dark matter (DM) and Barrow holographic dark energy (BHDE) whose IR cutoff is the apparent horizon. Among various DE models, (BHDE) model shows the dynamical enthusiasm to discuss the universe's transition phase. According to the new research, the universe transitioned smoothly from a decelerated to an accelerated period of expansion in the recent past. We exhibit that the development of $q$ relies upon the type of spatial curvature. Here we study the equation of state (EoS) parameter for the BHDE …
In this work, a way to consider together two originally different corrections to the Friedmann equations is presented. The first is the Barrow entropy, which imposes a fractal structure on the black hole horizon area. While the second is the well-known $f(R)$ gravity, which comes from a generalization of the Einstein-Hilbert action. Using the ideas of gravity-thermodynamics conjecture, these two models are combined. Then the modified Friedmann equation is obtained. Choosing a particular $f(R)$ model, an application is investigated. The state parameter and the density parameters for matter and …
