The paper deals with a theoretical model for interacting Tsallis holographic dark energy (THDE) whose infrared (IR) cut-off scale is set by the Hubble length. The interaction $Q$ between the dark sectors (dark energy and pressureless dark matter) of the universe has been assumed to be non-gravitational in nature. The functional form of $Q$ is chosen in such a way that it reproduces well known and most used interactions as special cases. We then study the nature of the THDE density parameter, the equation of state parameter, the deceleration parameter and the jerk parameter for this interacting THDE model. Our study shows that the universe exhibits the usual thermal history, namely the successive sequence of radiation, dark matter and dark energy epochs, before resulting in a complete dark energy domination in the far future. It is shown the evolution of the Hubble parameter for our model and compared that with the latest Hubble parameter data. Finally, we also investigate both the stability and thermodynamic nature of this model in the present context.
We discuss Tsallis holographic dark energy (THDE) model in higher dimension. An interacting dark energy model is proposed with Generalized Chaplygin Gas (GCG) in the framework of Compact Kaluza-Klein gravity. It is shown that a stable configuration can be found in the present epoch which is also compatible with the observed value of the density parameter. It is noted that dark energy (DE) might have evolved from a phantom phase in the past. Nature of dark energy is found to depend on the coupling parameter of the interaction. Classical stability consideration is also found to put an upper boun…
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 $f(R)$…
The $f(R)$ gravity theory is considered. It is a gravitational theory that generalizes the Einstein-Hilbert action. In this context, a holographic dark energy model is studied. Tsallis non-extensive entropy is used to introduce the dark energy density based on the holographic principle. Then the Friedmann equation, deceleration parameter, and equation of state for this model are investigated.
In this work, we study the evolution of a fractal universe composed of Tsallis holographic dark energy (THDE) and a pressureless dark matter that interact with each other through a mutual interaction. We then reconstruct the interaction term of this model by considering the Hubble length as the IR cut-off scale. We also study the behavior of different cosmological parameters during the cosmic evolution from the early matter-dominated era until the late-time acceleration. The present study shows that the universe undergoes a smooth transition from a decelerated to an accelerated phase of expans…
The manuscript presents the dynamics of Tsallis holographic dark energy (THDE) and Rényi holographic dark energy (RHDE) prescribed by a non-linear interaction in the FRW spacetime and for a scale factor evolving with a composite power law-exponential (hybrid) form. To construct the energy densities of these holographic dark energy models, I assume the Hubble cutoff to be the IR limit. I find that the deceleration parameter undergoes a signature flipping at a redshift $z$ consistent with observations. The EoS parameter $ω_{de}$ for both the HDE models exhibit quite contrasting dynamical behavio…
In this paper, we investigate a recent proposed model - so called the Tsallis holographic dark energy (THDE) model. In this case, we consider the non-gravitational and phenomenological interaction between dark sectors. We fit the free parameters of the model using Pantheon Supernovae Type Ia data, Baryon Acoustic Oscillations, Cosmic Microwave Background, Gamma-Ray burst and the the local value of the Hubble constant. We examine the THDE model to check its compatibility with observational data using objective Information Criterion (IC). We find that the THDE model cannot be supported by observ…
In this work, I framed the Renyi and Tsallis Holographic Dark Energy (HDE) models within the presence of a spatially flat and isotropic FRW model filled with matter and dark energy in teleparallel gravity. The energy densities of Renyi HDE and Tsallis holographic dark energy (THDE) are increasing functions of z and validate the expanding conduct of the universe. It is worthwhile to note that for -1<z<0, the EoS parameter of Renyi HDE approaches to phantom region , while THDE confirms to Quintessence region. Further for 0<z, the EoS parameter of Renyi HDE slants to CDM model ,while THDE settles…
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 …
In this work, we analyzed the effect of different prescriptions of the IR cutoffs, namely the Hubble horizon cutoff, particle horizon cutoff, Granda and Oliveros horizon cut off, and the Ricci horizon cutoff on the growth rate of clustering for the Tsallis holographic dark energy (THDE) model in an FRW universe devoid of any interactions between the dark Universe. Furthermore, we used the concept of configurational entropy to derive constraints (qualitatively) on the model parameters for the THDE model in each IR cutoff prescription from the fact that the rate of change of configurational entr…
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 work, we have illustrated the difference between both Tsallis and Kaniadakis entropies through cosmological models obtained from the formalism proposed by Padmanabhan, which is called holographic equipartition law. Similarly to the formalism proposed by Komatsu, we have obtained an extra driving constant term in the Friedmann equation if we deform the Tsallis entropy by Kaniadakis' formalism. We have considered initially Tsallis entropy as the Black Hole (BH) area entropy. This constant term may lead the universe to be in an accelerated mode. On the other hand, if we start with the Kan…
Using the generalized Tsallis entropy, the Tsallis holographic dark energy(THDE) was proposed recently. In this paper we analyze the cosmological consequences of the THDE model with an interaction between dark energy and dark matter $Q=H(αρ_{m}+βρ_{D})$. We find that the THDE model can explain the current accelerated cosmic expansion, and it is stable under certain conditions. Furthermore, through investigating the dynamical analysis, we find that there exists an attractor which represents an accelerated expansion phase of the universe. When $β=0$, this attractor corresponds to a dark energy d…
Towards a Machine Learning Solution for Hubble Tension: Physics-Informed Neural Network (PINN) Analysis of Tsallis Holographic Dark Energy in Presence of Neutrinos
In order to apply holography and entropy relations to the whole universe, which is a gravitational and thus nonextensive system, for consistency one should use the generalized definition for the universe horizon entropy, namely Tsallis nonextensive entropy. We formulate Tsallis holographic dark energy, which is a generalization of standard holographic dark energy quantified by a new dimensionless parameter $δ$, possessing the latter as a particular sub-case. We provide a simple differential equation for the dark energy density parameter, as well as an analytical expression for its equation-of-…
It has been found that the geometrical diagnostic methods can break the degeneracy for dark energy models. In this paper, we investigate the $Om$ diagnostic, the statefinder hierarchy $S_{n}$ and the composite null diagnostic $\{S_{n},ε\}$ for the Tsallis holographic dark energy models with interactions. We find that model parameters and the forms of interaction will influence the values of diagnostic parameters or the trends of the evolutionary trajectories for each model. Moreover, the statefinder hierarchy $S_{3}^{(1)}$ together with $\{S_{3}^{(1)},ε\}$ could give good diagnostic results. F…
We explore the effects of considering various infrared (IR) cutoffs, including the particle horizon, Ricci horizon and Granda-Oliveros (GO) cutoffs, on the properties of Tsallis holographic dark energy (THDE) model, proposed inspired by Tsallis generalized entropy formalism \cite{THDE}. Interestingly enough, we find that for the particle horizon as IR cutoff, the obtained THDE model can describe the accelerated universe. This is in contrast to the usual HDE model which cannot lead to an accelerated universe, if one consider the particle horizon as IR cutoff. We also investigate the cosmologica…
Employing the modified entropy-area relation suggested by Tsallis and Cirto \cite{non3}, and the holographic hypothesis, a new holographic dark energy (HDE) model is proposed. Considering a flat Friedmann-Robertson-Walker (FRW) universe in which there is no interaction between the cosmos sectors, the cosmic implications of the proposed HDE are investigated. Interestingly enough, we find that the identification of IR-cutoff with the Hubble radius, can lead to the late time accelerated Universe even in the absence of interaction between two dark sectors of the Universe. This is in contrast to th…
Using the Tsallis generalized entropy, holographic hypothesis and also considering the Hubble horizon as the IR cutoff, we build a holographic model for dark energy and study its cosmological consequences in the Brans-Dicke framework. At first, we focus on a non-interacting universe, and thereinafter, we study the results of considering a sign-changeable interaction between the dark sectors of the cosmos. Our investigations show that, compared with the flat case, the power and freedom of the model in describing the cosmic evolution is significantly increased in the presence of the curvature. T…
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,…
We apply the holographic principle in the cosmological context through the nonadditive Tsallis entropy, used to describe the thermodynamic properties of nonstandard statistical systems such as the gravitational ones. Assuming the future event horizon as the infrared cutoff, we build a dark energy model free from cosmological inconsistencies, which includes standard thermodynamics and standard holographic dark energy as a limiting case. We thus describe the dynamics of Tsallis holographic dark energy in a flat FLRW background. Hence, we investigate cosmological perturbations in the linear regim…
In this paper, by considering the complex form of the quintessence model, we study two different dynamic structures of holographic dark energy as Tsallis and Kaniadakis in the framework Brans-Dicke cosmology. In each setup, we employ non-interacting and interacting cases and calculate some cosmological parameters such as the equation of state $ω$. We also discuss the $ ω- ω'$ behavior. By modifying the potential and studying the scalar field dynamics, we examine the complex quintessence cosmology. In addition, considering the two parts of the quintessence field effects, i.e., real and complex,…
Using Tsallis statistics and its relation with Boltzmann entropy, the Tsallis entropy content of black holes is achieved, a result in full agreement with a recent study (Phys. Lett. B 794, 24 (2019)). In addition, employing Kaniadakis statistics and its relation with that of Tsallis, the Kaniadakis entropy of black holes is obtained. The Sharma-Mittal and Rényi entropy contents of black holes are also addressed by employing their relations with Tsallis entropy. Thereinafter, relying on the holographic dark energy hypothesis and the obtained entropies, two new holographic dark energy models are…
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…
In this paper, we use a Tsallis holographic dark energy model in two forms, interacting and non-interacting cases, to acquire some parameters as the equation of state for the energy density of the Tsallis model in the FRW universe concerning the complex form of quintessence model. We will study the cosmology of complex quintessence by revamping the potential and investigating the scalar field dynamics. Then we analyze ($ω-ω'$) and stability in two cases, i.e., non-interacting and interacting. We will explore whether these cases describe a real universe by calculating fractional energy density …
In this research, we are interested in constraining the nonlinear interacting and noninteracting Tsallis holographic dark energy (THDE) with Ricci horizon cutoff by employing three observational datasets. To this aim, the THDE with Ricci horizon considering the noninteraction and nonlinear interaction terms will be fitted by the SNe Ia, SNe Ia+H(z), and SNe Ia+H(z)+GRB samples to investigate the Hubble ($H(z)$), dark energy equation of state ($ω_{DE}$), effective equation of state ($ω_{eff}$), and deceleration ($q$) parameters. Investigating the $H(z)$ parameter illustrates that our models are…
We consider the interacting Tsallis Holographic Dark Energy (THDE), with the Granda-Oliveros (GO) scale as the infrared (IR) cutoff, as dynamical vacuum. We analytically solved for the Hubble parameter, in a spatially flat FLRW universe with dark energy and matter as components, and the solution traces the evolutionary path from the prior decelerated to the late accelerated epoch. Without interaction, the model predicts a $Λ$CDM like behavior with an effective cosmological constant. We used Pantheon Supernovae type Ia, observational Hubble data (OHD), cosmic microwave background (CMB), and bar…
In this paper, we investigate the dark energy phenomenon by studying the Tsallis holographic dark energy within the framework of Brans-Dicke (BD) scalar-tensor theory of gravity [Phys. Rev. \textbf{124}, 925 (1961)]. In this context, we choose the BD scalar field $ϕ$ as a logarithmic function of the average scale factor $a(t)$ and Hubble horizon as the IR cutoff ($L=H^{-1}$). We reconstruct two cases of non-interacting and interacting fluid (dark sectors of cosmos) scenario. The physical behavior of the models are discussed with the help of graphical representation to explore the accelerated e…
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, we obtain the law of emergence with Tsallis entropy from the thermodynamic laws. We first derive the law of emergence from the equilibrium description of the unified first law and Clausius relation. However, it has been shown that considering Tsallis entropy as the horizon entropy, the Clausius relation $δQ=T dS$ does not hold due to non-equilibrium thermodynamics and is replaced by the entropy-balance relation $dS=\frac{δQ}{T}+d_{i}S$, where $d_iS$ is the additional entropy produced due to the irreversible thermodynamic process. Hence, we derive the law of emergence from the no…
Black Hole Thermodynamics via Tsallis Statistical Mechanics and Phase Transitions Probed by Optical Characteristics
The Institute for Fundamental Study, Naresuan University（那莱素安大学基础研究所）；Quantum and Gravity Theory Research Group, Department of Physics, Faculty of Science, Ramkhamhaeng University（兰康亨大学理学院物理系量子与引力理论研究组）
The thermodynamics-gravity conjecture reveals that one can derive the gravitational field equations by using the first law of thermodynamics and vice versa. Considering the entropy associated with the horizon in the form of non-extensive Tsallis entropy, $S\sim A^β$ here we first derive the corresponding gravitational field equations by applying the Clausius relation $δQ=T δS$ to the horizon. We then construct the Friedmann equations of Friedmann-Lemaître-Robertson-Walker (FLRW) universe based on Tsallis modified gravity (TMG). Moreover, in order to constrain the cosmological parameters of TMG…
In this work, we use the statefinder parameter diagnostic to the Holographic principal inspired dark energy models, taking into consideration, the Tsallis Holographic dark energy (THDE) model, the standard Holographic dark energy (HDE) model, and the R$\acute{e}$nyi holographic dark energy (RHDE) model. The evolutionary behaviour of first statefinder $r(z)$, second statefinder parameter $s(z)$, the statefinder parameter pairs $(r, s)$ and $(r, q)$ as well as the deceleration parameter $q(z)$ are plotted for comparison for the various parameter values of the respective dark energy models. In th…
It is an old idea to realize Einstein's equations as a thermodynamical equation of state. Since then, there has been new conjectures to understand gravity from another point of view. In this way we can accept that the gravitational field is not an underlying one like an emergent force from other approaches based on the knowledge of relativity, quantum and black holes thermodynamics, and different statistical formalisms. One important question concerning this gravity/thermostatistics correspondence is whether the holographic screen could be well defined for a nonrelativistic case of a source ma…
We consider Tsallis cosmology as an approach to thermodynamic gravity and derive the bound on the Tsallis parameter to be $β<2$ by using the constraints derived from the formation of the primordial light elements, Helium, Deuterium and Litium, from the observational data from Big Bang Nucleosynthesis (BBN) which allows only a very tiny deviation from General Relativity (GR). Next we consider thermal dark matter (DM) freeze-out mechanism in Tsallis cosmological era and derive bounds on the Tsallis parameter from the observed DM relic abundance to be $1-β< 10^{-5}$.
Recently, the Rényi and Tsallis generalized entropies have extensively been used in order to study various cosmological and gravitational setups. Here, using a special type of generalized entropy, a generalization of both the Rényi and Tsallis entropy, together with holographic principle, we build a new model for holographic dark energy. Thereinafter, considering a flat FRW universe, filled by a pressureless component and the new obtained dark energy model, the evolution of cosmos has been investigated showing satisfactory results and behavior. In our model, the Hubble horizon plays the role o…
In this article, we investigate the thermodynamic stability of the FRW universe for two examples, Tsallis entropy and loop quantum gravity, by considering non-extensive statistical mechanics. The heat capacity, free energy and pressure of the universe are obtained. For the Tsallis entropy model, we obtained the constraint for $β$, namely, $1/2 < β< 2$. The free energy of a thermal equilibrium universe must be less than zero. We suggest that the reason for the accelerated expansion of the universe is not due to Tsallis entropy. Similar results are obtained for loop quantum gravity. However, sin…
Gravity is so different from other fundamental forces that it is now essentially treated as a non-fundamental force of entropic origin. A number of good studies have been carried out in this direction. Quantum gravity has also significantly improved our understanding by combining gravity well with quantum physics. However, there are still many impediments to our understanding especially in the limits of extreme. The effects of quantum gravity start appearing on the scene at Planck length which is the smallest length in nature idealized so far. While as this study incorporates a model which is …
In this paper we employ a recent proposal of C. Tsallis and formulate the first law of thermodynamics for gravitating systems in terms of the extensive but non-additive entropy. We pay a particular attention to an integrating factor for the heat one-form and show that in contrast to conventional thermodynamics it factorizes into thermal and entropic part. Ensuing first law of thermodynamics implies Tsallis cosmology, which is then subsequently used to address the observed discrepancy between current bound on the Dark Matter relic abundance and present IceCube data on high-energy neutrinos. To …
Recently, Verlinde conjectured that gravity may be an entropic force, arising from thermodynamics on the holographic screen. We investigate the implications of the entropic force formalism for inflationary cosmology. We find the background dynamics of inflation can be dually described in the holographic language. At the perturbation level, two kinds of novel scale invariant scalar fluctuations arise from thermal fluctuations on the holographic screen. These fluctuations can be responsible for CMB anisotropy and structure formation.
We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis' non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press (cond-mat/0204315)) have revealed that the extremum-state of Tsallis entropy characterized by the so-called stellar polytrope has consistent thermodynamic structure, which predicts the thermodynamic instability due to the negative specific heat. However, their analyses heavily relies on the old Tsallis formalism using standard linear mean values. In this paper, e…
