I. Brevik, A. V. Timoshkin
We describe the evolution of the early and late universe from thermodynamic considerations, using the generalized non-extensive Tsallis entropy with a variable exponent. A new element in our analysis is the inclusion of a bulk viscosity in the description of the cosmic fluid. Using the generalized Friedmann equation, a description of the early and the late universe is obtained.
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Cosmology from Transactional Entropic Gravity: A Concise Review
综述交易熵引力模型中暗物质、暗能量及宇宙学矛盾的关键方面，提出新的理论框架以解释观测现象。
Entropic Gravity and Cosmology in Kaniadakis Statistics
本研究利用Kaniadakis统计，基于Verlinde引力熵形式修正牛顿引力与径向速度分布，发现结合该非广延统计下的弗里德曼第一方程可得到加速宇宙，为引力与宇宙学研究提供新视角。
On entropic cosmology, late time acceleration and the quantum bounce
该研究提出圈量子宇宙学中量子反弹与暗能量的统一熵描述，推导弗里德曼方程并证实二者的熵起源。
We investigate a possibility of realizing the entropic force into the cosmology. A main issue is how the holographic screen is implemented in the Newtonian cosmology. Contrary to the relativistic realization of Friedmann equations, we do not clarify the connection between Newtonian cosmology and entropic force because there is no way of implementing the holographic screen in the Newtonian cosmology.
Modified gravity as entropic cosmology
本工作揭示了修正引力理论与基于表观视界热力学的熵宇宙学之间的直接对应关系，表明具有多个热力学自由度的修正引力需推广热力学定律，其视界熵自然包含Bekenstein-Hawking熵的时间导数项。
It has been recently proposed that gravity might be an entropic force. Although a well defined fundamental description for such a mechanism is still lacking, it is still possible to address the viability of phenomenological models of entropic-inspired modified gravities. I will summarize some recent work directed to using cosmology as a tool to constraint scenarios in which the modifications are aimed to explain the physics behind dark energy and inflation. A phenomenological modification is able to explain cosmic acceleration at the background level and fit observations, but simple inflation …
In this paper we discuss some consequences of cosmological models in which the primordial cosmic matter is described by a relativistic imperfect fluid. The latter takes into account the dissipative effects (bulk viscosity) arising from different cooling rates of the fluid components in the expanding Universe. We discuss, in particular, the effects of the bulk viscosity on Big Bang Nucleosynthesis and on the thermal relic abundance of particles, looking at recent results of PAMELA experiment. The latter has determined an anomalous excess of positron events, that cannot be explained by the conve…
Inhomogeneous cosmological models such as the Stephani universes could, in principle, provide an explanation for the observed accelerated expansion of the Universe. Working with a concrete, popular model of the Stephani cosmology -- the Stephani-Dabrowski model, we found that it is entropically viable. We also comment on the energy conditions and the two-sheeted geometry of the spacetime. However, similar to the LTB models, despite satisfying the holographic principle, Stephani cosmology has difficulty satisfying all the constraints from observations.
We study a cosmology by considering entropic issues. We make a bare/effective description of the equation of state of the cosmic fluid through a bare (ω)/effective (ω_eff) conservation equation. In the bare case, where we have a non conserved equation of state for the cosmic fluid, we describe the change in the sign of the inhomogeneus term at different times of the cosmic evolution. We show that by a redefinition of the adiabatic ω-parameter we can recover the usual scheme for the cosmic evolution. In the effective case we show also that if the evolution is driven by dust or cosmological cons…
We analyze the thermodynamical consistency of entropic-force cosmological models. Our analysis is based on a generalized entropy scaling with an arbitrary power of the Hubble radius. The Bekenstein-Hawking entropy, proportional to the area, and the nonadditive $S_{δ=3/2}$-entropy, proportional to the volume, are particular cases. One of the points to be solved by entropic-force cosmology for being taken as a serious alternative to mainstream cosmology is to provide a physical principle that points out what entropy and temperature have to be used. We determine the temperature of the universe ho…
Exploring Rényi Entropic Cosmology Constrained by DESI DR2 BAO and Complementary Late-Time Observations
本文基于瑞尼熵修正的弗里德曼方程构建宇宙模型，并利用DESI、P-BAO、CC和引力波观测数据对模型进行约束，得出瑞尼参数λ的严格限制，且结果符合大爆炸核合成和重子生成学界限制。
Anisotropic cosmology in $q$-deformed entropic gravity
本文在Verlinde熵引力框架下研究q-变形理论对各向异性Bianchi I型宇宙学模型的影响，推导了受q-变形影响的动力学方程并分析其轴对称解，揭示了q-变形对早期宇宙演化的潜在作用。
We derive the MOND cosmology which is uniquely corresponding to the original MOND at galaxy scales via entropic gravity method. It inherits the key merit of MOND, that is, it reduces the baryonic matter and non-baryonic dark matter into baryonic matter only. For the first time we obtain the critical parameter in MOND, i.e., the transition acceleration $a_c$ at cosmological scale. We thus solve the long-standing coincidence problem $a_c\sim cH_{0}$. More interestingly, a term like age-graphic dark energy emerges naturally. In the frame of this MOND cosmology, we only need baryonic matter to des…
Mass-to-Horizon Entropic Cosmology: A Unified Thermodynamic Pathway to Cosmic Acceleration
该研究提出基于熵力的宇宙加速模型，通过多观测数据联合分析，证明熵起源可解释晚期宇宙加速，优于ΛCDM模型。
Cosmic acceleration in entropic cosmology
本研究提出带体积熵项的修正熵-面积关系推导的熵宇宙学模型，解释晚期宇宙加速，经观测数据验证符合观测，且与膜世界宇宙学模型等价。
We study particle creation in the presence of bulk viscosity of cosmic fluid in the early universe within the framework of open thermodynamical systems. Since the first-order theory of non-equilibrium thermodynamics is non-causal and unstable, we try to solve the bulk viscosity equation of the cosmic fluid with particle creation through the full causal theory. By adopting an appropriate function for particle creation rate of "Creation of Cold Dark Matter" model, we obtain analytical solutions which do not suffer from the initial singularity and are in agreement with equivalent solutions of Lam…
Based on the assumptions of the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electroweak transition has occurred at approximately $10μ$ seconds after the Big Bang to convert a plasma of free quarks and gluons into hadrons. We consider such a phase transition in the context of a deformed Horava-Lifshitz cosmology. The Friedmann equation for the deformed Horava-Lifshitz universe is obtained using the entropic interpretation of gravity, proposed by Verlinde. We investigate the effects of the parameter $ω$ appearing in the theory on the evoluti…
We investigate entropic force cosmological models with the possibility of matter creation and energy exchange between the bulk and the horizon of a homogeneous and an isotropic flat Universe. We consider three different kinds of entropy, Bekenstein's, the non-extensive Tsallis-Cirto's and the quartic entropy, plus some phenomenological functional forms for matter creation rate to model different entropic force models and put the observational constraints on them. We show that while most of them are basically indistinguishable from a standard $Λ$CDM scenario, the Bekenstein entropic force model…
Growth of Cosmic Structures in generalized mass-to-horizon relation Entropic Cosmology
本文研究了广义质量与视界关系熵宇宙学（MHEC）中宇宙结构的增长，推导了线性扰动方程，发现其无需额外自由参数即可与 LCDM 一样匹配背景与增长探针，为宇宙加速膨胀提供了可行的熵解释。
Multidimensional cosmological model describing the evolution of a fluid with shear and bulk viscosity in $n$ Ricci-flat spaces is investigated. The barotropic equation of state for the density and the pressure in each space is assumed. The second equation of state is chosen in the form when the bulk and the shear viscosity coefficients are inversely proportional to the volume of the Universe. The integrability of Einstein equations reads as a colinearity constraint between vectors which are related to constant parameters in the first and second equations of state. We give exact solutions in a …
The correspondence of generalised entropic cosmology theory with $F(T)$ and $F(Q)$ modified gravity and gravitational waves
本研究通过类比Jacobson从贝肯斯坦-霍金熵推导爱因斯坦方程的工作，探究修改引力与广义熵宇宙学的对应关系，证实$F(T)$、$F(Q)$引力与广义熵引力的对应，指出其引力波方程与爱因斯坦引力一致仅耦合项被修正，Tsallis熵情形下耦合变化会影响引力波辐射强度。
Different aspects of entropic cosmology
本文回顾了基于表观视界热力学定律的熵宇宙学，阐述第一定律如何联系修正引力与视界熵，并利用第二定律给出模型无关约束，进而讨论其对暴胀、再加热和原初引力波的影响。
The causal entropic principle aims to predict the unexpectedly small value of the cosmological constant Lambda using a weighting by entropy increase on causal diamonds. The original work assumed a purely isotropic and homogeneous cosmology. But even the level of inhomogeneity observed in our universe forces reconsideration of certain arguments about entropy production. In particular, we must consider an ensemble of causal diamonds associated with one cosmology, and we can no longer immediately discard entropy production in the far future of the universe. Depending on our choices for a probabil…
We explore the cosmological models of the late-time universe based on the holographic principle, taking into account the properties of the viscosity of the dark fluid. We use the mathematical formalism of generalized infrared cutoff holographic dark energy, as presented by Nojiri and Odintsov (2017). We consider the Little Rip, the Pseudo Rip, and a bounce exponential model, with two interacting fluids, namely dark energy and dark matter in a spatially-flat Friedmann-Robertson-Walker universe. Within these models, analytical expressions are obtained for infrared cutoffs in terms of the particl…
We investigate thermal inflation in double-screen entropic cosmology. We find that its realization is general, resulting from the system evolution from non-equilibrium to equilibrium. Furthermore, going beyond the background evolution, we study the primordial curvature perturbations arising from the universe interior, as well as from the thermal fluctuations generated on the holographic screens. We show that the power spectrum is nearly scale-invariant with a red tilt, while the tensor-to-scalar ratio is in agreement with observations. Finally, we examine the non-Gaussianities of primordial cu…
Dark energy era with a resolution of Hubble tension in generalized entropic cosmology
本文提出基于四参数广义熵的暗能量模型，通过推广表观视界熵描述宇宙热历史，并在特定参数下给出更高哈勃常数，从而为缓解哈勃张力提供可行方案。
We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant $G$ and the speed of light $c$. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework are given and one of them is tested against combined observational data (supernovae, BAO, and CMB). From the fit of the data it is found that the Hawking temperature numerical coefficient $γ$ is two to four orders of magnitude less than usually assumed on the geometrical ground theoretical value of $O(1)$ …
We propose a new five-parameter entropy function that proves to be singular-free during the entire cosmic evolution of the universe, and at the same time, also generalizes the Tsallis, Barrow, Rényi, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies for suitable limits of the parameters. In particular, all the above mentioned known entropies become singular (or diverge) when the Hubble parameter vanishes in course of the universe's evolution (for instance, in bounce cosmology at the instant of bounce), while the newly proposed entropy function seems to be singular-free even at $H = …
Observational constraints on entropic cosmology
本文基于含体积、线性、对数及新熵修正的熵-面积关系，推导广义修正弗里德曼方程，并用哈勃参数、重子声学振荡和强透镜数据约束参数，发现模型与低红移观测及SH0ES的H0值相容。
ACT-DR6 consistent inflation in generalised entropic cosmology and $f(Q)$ gravity
在广义熵宇宙学和$f(Q)$引力框架下，通过重构方案构建暴胀模型，经ACT-DR6等数据检验，还研究了与标量耦合情况，通过选择标量势获得一致暴胀，其发现或指向早期宇宙正确统一熵。
Observational constraints on Luciano-Saridakis entropic cosmology
本文通过观测数据检验了Luciano-Saridakis提出的广义熵理论，发现其在背景层面能够稳健地拟合多种数据集，并在不违反标准模型的情况下缓解哈勃张力。
We analyze the dynamics of a Bianchi I cosmology in the presence of a viscous fluid, causally regularized according to the Lichnerowicz approach. We show how the effect induced by shear viscosity is still able to produce a matter creation phenomenon, meaning that also in the regularized theory we address, the Universe is emerging from a singularity with a vanishing energy density value. We discuss the structure of the singularity in the isotropic limit, when bulk viscosity is the only retained contribution. We see that, as far as viscosity is not a dominant effect, the dynamics of the isotropi…
Holography is expected as one of the promising descriptions of quantum general relativity. We present a model for a cosmological system involving two holographic screens and find that their equilibrium exactly yields a standard Friedmann-Robertson-Walker universe. We discuss its cosmological implications by taking into account higher order quantum corrections and quantum nature of horizon evaporation. We will show that this model could give rise to a holographic inflation at high energy scales and realize a late-time acceleration in a unified approach. We test our model from the SN Ia observat…
We consider how the five-dimensional Randall-Sundrum (one-brane) theory becomes modified when account is taken of the bulk viscosity of the cosmic fluid on the brane. We focus on the plasma era between $10^{12}$K (muon pair annihilation) to about $5\times 10^9$K (electron-positron annihilation), which includes the first order quark-hadron transition beginning at an energy density of about $5\times 10^9\rm MeV^4$. Various possibilities are examined for modeling the bulk viscosity, preference being at the end given to the results calculated from relativistic kinetic theory. According to this, th…
Origin of bulk viscosity in cosmology and its thermodynamic implications
本文提出宇宙共动膨胀速度梯度导致体黏滞性的新机制，并证明含体黏滞性的宇宙演化自然满足表观视界热力学第一和第二定律，从而确立了黏性宇宙学的热力学对应关系。
In this work, we present a phase space analysis of a spatially flat Friedmann $-$Robertson$-$Walker (FRW) model in which the dark matter fluid is modeled as an imperfect fluid having bulk viscosity. The bulk viscosity is governed by the Maxwell$-$Cattaneo approach. The rest of the components of the model: radiation and dark energy are treated as perfect fluids. Imposing a complete cosmological dynamics and taking into account a recent constraint on the dark matter equation of state (EOS), we obtain bound on the bulk viscosity. The results point towards the possibility of describing not only th…
Holographic realization from inflation to reheating in generalized entropic cosmology
本文基于四参数广义熵$S_\mathrm{g}$，在熵能量密度作为暴胀子的框架下，研究了宇宙从暴胀到重加热的演化，证实其符合Planck数据并实现了Hubble参数的连续相变。
Primordial gravitational waves in horizon cosmology and constraints on entropic parameters
本研究从暴胀期产生的原初引力波视角出发，探究4参数广义熵的参数约束问题，验证了特定熵参数范围可实现宇宙平滑演化，且对应原初引力波谱有望被未来观测站探测，为广义熵参数测量提供新途径。
It has been recently proposed that the interpretation of gravity as an emergent, entropic force might have nontrivial implications to cosmology. Here two approaches are investigated: in one, the Friedman equation receives entropic contributions from the usually neglected surface terms, and in another, the extra terms are derived from quantum corrections to the entropy formula. UV terms may drive inflation, avoiding a recently derived no-go theorem, though in some cases leading to a graceful exit problem. IR terms can generate dark energy, alleviating the cosmological constant problem. The quan…
The growing interest of different entropy functions proposed so far (like the Bekenstein-Hawking, Tsallis, Rényi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies) towards black hole thermodynamics as well as towards cosmology lead to the natural question that whether there exists a generalized entropy function that can generalize all these known entropies. With this spirit, we propose a new 4-parameter entropy function that seems to converge to the aforementioned known entropies for certain limits of the entropic parameters. The proposal of generalized entropy is extended …
Entropic cosmology assumes several forms of entropy on the horizon of the universe, where the entropy can be considered to behave as if it were related to the exchange (the transfer) of energy. To discuss this exchangeability, the consistency of the two continuity equations obtained from two different methods is examined, focusing on a homogeneous, isotropic, spatially flat, and matter-dominated universe. The first continuity equation is derived from the first law of thermodynamics, whereas the second equation is from the Friedmann and acceleration equations. To study the influence of forms of…
We investigate the effects of the accretion of phantom energy with non-zero bulk viscosity onto a Morris-Thorne wormhole. We have found that if the bulk viscosity is large then the mass of wormhole increases rapidly as compared to small or zero bulk viscosity.
Cosmological Tensions with Non-Extensive Entropic Cosmology: A Modified Stress-Energy Approach
本文提出修正能量-动量张量框架，分析 Tsallis、Rényi 和 Kaniadakis 非广延熵宇宙学的宇宙学参数，并探讨其缓解约 5σ Hubble 张力的潜力。
Singularities in the dark energy universe are discussed, assuming that there is a bulk viscosity in the cosmic fluid. In particular, it is shown how the physically natural assumption of letting the bulk viscosity be proportional to the scalar expansion in a spatially flat FRW universe can drive the fluid into the phantom region (w < -1), even if lies in the quintessence region (w > -1) in the non-viscous case.
Penrose [1] has emphasized how the initial big bang singularity requires a special low entropy state. We address how recent brane cosmological schemes address this problem and whether they offer any apparent resolution. Pushing the start time back to $t=-\infty$ or utilizing maximally symmetric AdS spaces simply exacerbates or transfers the problem. Because the entropy of de Sitter space is $S\leq 1/Λ$, using the present acceleration of the universe as a low energy $(Λ\sim 10^{-120}$) inflationary stage, as in cyclic ekpyrotic models, produces a gravitational heat death after one cycle. Only h…
Entropy applications in cosmology: spacetime thermodynamics, holographic dark energy, entropic gravity and beyond - a review
本综述统一阐述熵在引力与宇宙学中的作用，涵盖黑洞热力学、全息原理、时空热力学猜想、全息暗能量及熵引力，旨在厘清熵的角色并指出未来研究方向。
Entropic Chaplygin-Gas cosmology and late-universe tension diagnostics
研究早期与晚期宇宙测量差异下，熵广义查普利金气体宇宙学对参数简并性的影响。通过多种数据约束模型，发现其能再现ΛCDM背景膨胀并改变参数区域，减少背景驱动差异，支持$H_0$和$S_8$张力源于不同物理扇区的可能性。
In this paper, we investigate the viscous modified Chaplygin gas cosmological model. Solutions for different values of the viscosity parameter are obtained using both analytical and numerical methods. We have calculated the deceleration and defined {\em newly} statefinder $\{r, s \}$ pair in D dimensions. It is shown that when $D=4$, the usual statefinder parameters are recovered. Furthermore, we apply the statefinder diagnostic to the MCG model with and without viscosity in $D$ dimensions and explore these parameters graphically.
We calculate new corrections to the Brane-world dynamics, lying in a 5D Schwarzschild-De Sitter black hole, generalizing the result of Nojiri, Odintsov and Ogushi (NOO) in Ref.\cite{Nojiri:2002vu}, The NOO entropy effect is based on the Logharitmic correction to the bulk entropy firstly calculated by Mukherji and Pal in Ref.\cite{Mukherji:2002de}. We calculate higher order contributions to the brane worldsheet. The extra terms obtained lead to interesting implications in brane-cosmology. In particular, new entropic terms rapidly disappear in the late Universe while exploding in the very Early …
We study the effect of the inclusion of bulk brane viscosity on brane world (BW) cosmology in the framework of the Eckart's theory, we focus in the Randall-Sundrum model with negative tension on the brane.
We discuss influences of bulk viscosity on the Early Universe, which is modeled by Friedmann-Robertson-Walker metric and Einstein field equations. We assume that the matter filling the isotropic and homogeneous background is relativistic viscous characterized by ultra-relativistic equations of state deduced from recent lattice QCD simulations. We obtain a set of complicated differential equations, for which we suggest approximate solutions for Hubble parameter $H$. We find that finite viscosity in Eckart and Israel-Stewart fluids would significantly modify our picture about the Early Universe.
D-dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing both shear and bulk viscosity in n Ricci-flat spaces is investigated. The second equations of state are chosen in some special form of metric dependence of the shear and bulk viscosity coefficients. The equations of motion are integrated and the dynamical properties of the exact solutions are studied. It is shown the possibility to resolve the cosmic coincidence problem when the x-fluid plays role of quintessence and the viscous fluid is used as cold dark matter.
Fitting NANOGrav 15-year data and ACT data with modified inflation in entropic cosmology
本文通过修正的熵宇宙学膨胀模型，拟合NANOGrav 15年数据和ACT数据，以解释随机引力波背景与观测数据的兼容性。
The irrotational Bianchi V cosmological model under the influence of both shear and bulk viscosity, together with heat flux, has been studied. Exact solutions for the model are obtained with three physically viable assumptions. The first two relate the matter density, shear scalar, and expansion scalar and the third is a barotropic equation of state, connecting the matter density and thermodynamic pressure. The properties of the solutions are studied and the temperature distribution is also presented explicitly. It has been observed that along with the viscosity, heat flux further adds to the …
We present a discussion of the effects induced by bulk viscosity on the very early Universe stability. The viscosity coefficient is assumed to be related to the energy density $ρ$ via a power-law of the form $ζ=ζ_0 ρ^s$ (where $ζ_0, s=const.$) and the behavior of the density contrast in analyzed. In particular, we study both Einstein and hydrodynamic equations up to first and second order in time in the so-called quasi-isotropic collapsing picture near the cosmological singularity. As a result, we get a power-law solution existing only in correspondence to a restricted domain of $ζ_0$. The par…
From a hydrodynamicist's point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (excluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review we discuss a variety of topics in cosmology when i…
Perturbations with bulk viscosity in modified chaplygin gas cosmology
本文利用1+3协变形式理论研究粘性修正Chaplygin气体模型的宇宙学扰动，通过数值求解长波和短波极限下的扰动方程，发现能量过密度对比度随红移衰减，且其结果与ΛCDM存在显著差异。
Constraints on Kaniadakis Cosmology from Starobinsky Inflation and Primordial Tensor Perturbations
本文研究了通过将引力热力学猜想应用于宇宙视界而得到的广义熵宇宙学，探讨了其对早期宇宙物理的影响，特别是原初引力波和慢-roll膨胀在Starobinsky-like场景中的意义，并通过Planck和BICEP/Keck观测数据对Kaniadakis参数进行了严格约束。
Entropic Inflation in Presence of Scalar Field
本研究提出在广义视界熵框架下，引入最小耦合标量场，使被排除的$\phi^2$势重新可行，实现有出口的膨胀宇宙学。
In this paper we present two concrete models of non-perfect fluid with bulk viscosity to interpret the observed cosmic accelerating expansion phenomena, avoiding the introduction of exotic dark energy. The first model we inspect has a viscosity of the form $ζ = ζ_0 + (ζ_1-ζ_2q)H$ by taking into account of the decelerating parameter q, and the other model is of the form $ζ = ζ_0 + ζ_1H + ζ_2H^2$. We give out the exact solutions of such models and further constrain them with the latest Union2 data as well as the currently observed Hubble-parameter dataset (OHD), then we discuss the fate of unive…
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