• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Theoretical aspects of holographic dark energy

    2023-05-12 20:43:45ShuangWangandMiaoLi
    Communications in Theoretical Physics 2023年11期

    Shuang Wang and Miao Li

    School of Physics and Astronomy,Sun Yat-Sen University,Zhuhai,China

    Abstract We review the theoretical aspects of holographic dark energy (HDE) in this paper.Making use of the holographic principle (HP) and the dimensional analysis,we derive the core formula of the original HDE (OHDE) model,in which the future event horizon is chosen as the characteristic length scale.Then,we describe the basic properties and the corresponding theoretical studies of the OHDE model,as well as the effect of adding dark sector interaction in the OHDE model.Moreover,we introduce all four types of HDE models that originate from HP,including (1) HDE models with the other characteristic length scale;(2) HDE models with extended Hubble scale;(3) HDE models with dark sector interaction;(4) HDE models with modified black hole entropy.Finally,we introduce the well-known Hubble tension problem,as well as the attempts to alleviate this problem under the framework of HDE.From the perspective of theory,the core formula of HDE is obtained by combining the HP and the dimensional analysis,instead of adding a DE term into the Lagrangian.Therefore,HDE remarkably differs from any other theory of DE.From the perspective of observation,HDE can fit various astronomical data well and has the potential to alleviate the Hubble tension problem.These features make HDE a very competitive dark energy scenario.

    Keywords: holographic principle,dark energy,holographic dark energy

    1.Introduction

    The holographic principle (HP) [1,2],which was inspired by the black hole thermodynamics [3,4],reveals that all the physical quantities located in a volume of space can be represented by some physical quantities located on the boundary of that space.After the discovery of the Antide Sitter/Conformal field theories (AdS/CFT) correspondence [5],it is widely believed that the HP should be a fundamental principle of quantum gravity.So far,the HP has been applied to various fields of physics,including nuclear physics [6],condensed matter physics [7],theoretical physics[8] and cosmology [9].

    In this paper we focus on the dark energy (DE) problem[10,11].The most popular theoretical model is the ΛCDM model,which includes a cosmological constant Λ and a cold dark matter (CDM) component.But the ΛCDM model has two cosmological constant problems [12–20]: (a) Why ρΛ≈0? (b) Why ρΛ~ρmnow? In the past 25 years,hundreds of DE models have been proposed;however,so far the nature of DE is still a mystery.

    In essence,the DE problem should be an issue of quantum gravity.Since the HP is the most fundamental principle of quantum gravity,it may also has great potential to solve the DE problem.In 2004,by applying the HP to the DE problem,One of the present authors (Miao Li) proposed a new DE model,i.e.holographic dark energy(HDE) model [21].The DE energy density ρdeof this model only relies on two physical quantities: (1) the reduced Planck massMp≡where G is the Newton constant;(2) the cosmological length scale L,which is chosen as the future event horizon of the Universe[21].Note that this model is the first DE model inspired by the HP [22].From now on,we will call it the original HDE(OHDE) model.

    So far,the idea of applying the HP to the DE problem has drawn a lot of attention:

    1.To explain the origin of HDE,many different theoretical mechanisms are proposed;

    2.To consider the interaction between dark sectors,the interacting HDE models are studied;

    3.A lot of other HDE models are proposed,where different forms of L are taken into account.

    4.Some attempts are made,to alleviate the Hubble tension problem under the framework of HDE.

    In this paper,all the topics mentioned above will be reviewed.We assume today’s scale factor a0=1,where the subscript ‘0’ always indicates the present value of the physical quantity.In addition,we use the metric convention(-,+,+,+),as well as the natural units c=?=1.

    2.The basic of cosmology

    This section introduces the basics of cosmology,including the Friedmann–Lema?tre–Robertson–Walker (FLRW) cosmology,as well as the DE problem.

    2.1.Friedmann–Lema?tre–Robertson–Walker cosmology

    Modern cosmology has two cornerstones.The first cornerstone is general relativity (GR),whose core is the Einstein field equation

    Note that Gμνis the Einstein tensor,Rμνis the Ricci tensor,R is the Ricci scalar,gμνis the metric,and Tμνis the energy-momentum tensor.In addition,Tμν=(ρ+p)uμuν+gμνp,where ρ and p are the total energy density and the total pressure of all the components,respectively.

    The second cornerstone is the cosmological principle,i.e.the Universe is homogeneous and isotropic on large scales.It means that the Universe should be described by the FLRW metric

    Note that t is the cosmic time,a(t) is the scale factor,r is the spatial radius coordinate,Ω2is the two-dimensional unit sphere volume,and the quantity k characterizes the curvature of three-dimensional space.

    Based on equations (1) and (2),two Friedmann equations can be obtained

    HereH≡is the Hubble parameter,which denotes the expansion rate of the Universe.

    From these two Friedmann equations,one can see that the pressure p affects the expansion of the Universe: if p >-ρ/3,the Universe will decelerate;if p <-ρ/3,the Universe will accelerate.Moreover,if all the components in the Universe were determined,the expansion history of the Universe would be determined too.

    2.2.Dark energy problem

    Let us start from a short introduction to the history of the DE problem.In 1917,to maintain a static Universe,Einstein added a cosmological constant Λ in the Einstein field equations [23].Afterwards,because of the discovery of cosmic expansion,Einstein declared that this was the biggest mistake he made in his whole career.In 1967,Zel’dovich reintroduced the cosmological constant by taking the vacuum fluctuations into account [24].In 1998,Two astronomical teams discovered the accelerating expansion of the Universe[10,11],which declares the return of DE.

    As is well known,the Universe has four main components: baryon matter,DM,radiation,and DE.So the first Friedmann equation satisfies

    where w ≡pde/ρdeis the DE equation of state (EoS) [25–30].As mentioned above,in the past 25 years hundreds of DE models have been proposed;different DE models will yield different forms of EoS.

    In 1989,Weinberg published a review article of DE,which divided various DE models into five categories [31]:

    1.Symmetry.This category includes many theoretical attempts,such as no-scale supersymmetry [32] and complexification of coordinates [33].

    2.Anthropic principle.The key idea is a multiverse,where different DE energy densities can be realized [34,35].We live in a universe with the observed DE density,because it allows long enough time for galaxy formation.The discovery of string landscape [36,37] support this idea.

    3.Tuning mechanisms.This category introduces a scalar field which can reduce the DE energy density.Some models of this category result in vanishing Newton’s constant [38,39].

    4.Modified gravity.By modifying the left side of Einstein’s field equations,modified gravity can also explain cosmic acceleration.There are a large number of modified gravity models,such as unimodular gravity [40,41] and massive gravity [42].

    5.Quantum gravity.Making use of the Hartle-Hawking wave function of the Universe [43],a small DE energy density is predicted [44].

    Afterward,some new theoretical DE models were proposed.Therefore,three new categories can be added [18]:

    6.Holographic principle.This is the Key point of this review.

    7.Back-reaction of gravity.Under the frame of general relativity,inhomogeneities of the Universe can backreact on the FLRW background [45].

    8.Phenomenological models.It is argued that DE can be described by scalar fields with various potentials or kinetic terms [14].

    In this paper,we just focus on the sixth category,i.e.holographic principle.

    3.Original holographic dark energy model

    In this section,we introduce how to apply the HP to the DE Problem.

    3.1.General formula of HDE energy density

    Now let us take into account the Universe with a characteristic length scale L.Based on the HP,one can conclude that the DE energy density ρdecan be described by some physical quantities on the boundary of the Universe.Obviously,one can only use the reduced Planck mass Mpand the cosmological length scale L to construct ρde.Making use of the dimensional analysis,we can obtain

    where C1,C2,C3are dimensionless constant parameters.Note that the first term is 10120times larger than the cosmological observations [12],so this term should be deleted (For a more theoretical analysis,see [46]).Moreover,compared with the second term,the third and the other terms are negligible,so these terms should be deleted,too.

    Therefore,the expression of ρdecan be written as

    where C is the dimensionless constant parameter,too.It must be stressed that equation (8) is the general formula of HDE energy density.In other words,all the DE models of the sixth category can give an energy density form that is the same as equation (8).

    3.2.The original HDE model

    After deriving the general formula of the HDE energy density,one needs to choose the specific form of the characteristic length scale L.The simplest choice,i.e.the Hubble scale L=1/H [47,48],will yield a wrong EoS of DE [49].Besides,the particle horizon is not a good choice either,because it cannot yield cosmic acceleration.

    In 2004,Li suggested that the characteristic length scale L should be chosen as the future event horizon [21]

    This is the first HDE model that can yield cosmic acceleration,So we call it the original HDE (OHDE) model.

    For the OHDE model,the Friedmann equation satisfies

    or equivalently,

    whereρc≡is the critical density of the Universe.Taking the derivative of Ωde,and making use of equation (9),one can obtain

    where the prime denotes derivative with respect tolna.From equation (10),we have

    Based on equations (13) and (14),one can obtain

    This equation describes the dynamical evolution of the OHDE model.Since 0 <Ωde<1,dΩde/dz is always negative,namely the fraction density of HDE always increases along with redshift z →-1.Based on equations (15) and (11),one can obtain the redshift evolution of Hubble parameter H(z) of the OHDE model.

    3.3.Important properties of the OHDE model

    · EoS

    Energy conservation tells us that

    Based on equations (8) and (17),one can obtain the EoS of the OHDE model

    In the early Universe with Ωde?1,w ?-1/3,thus Ωde~a-2.In the late Universe with Ωde?1,w ?-1/3 -2/3C,thus cosmic acceleration will be yielded as long as C >0.Moreover,if C=1,w=-1,then HDE will be close to the cosmological constant;if C >1,w >-1,then HDE will be a quintessence DE [50];if C <1,w <-1 thus HDE will be a phantom DE [51–53].

    · The Coincidence Problem

    The coincidence problem is equivalent to a problem of why the ratio between the DE density and the radiation density is so tiny at the beginning of the radiation-dominated epoch [54].

    Let us consider the inflation epoch,which has two main components: the HDE and the inflation energy.Note that the inflation energy is almost constant during the inflation epoch,and then decayed into radiation after the inflation.

    If the inflation energy scale is 1014Gev,the ratio between ρdeand ρris about 10-52[21].During the inflation epoch,the HDE is diluted as Ωde~a-2,this is equivalent to (N)exp -2 with N=60.This means that the OHDE model can explain the coincidence problem,as long as the inflation epoch lasts for 60 e-folds [55].

    4.Theoretical motivations for the OHDE model

    In addition to the dimensional analysis mentioned above,some other theoretical motivations can also lead to the general formula of HDE energy density.Here we review some related research works.

    4.1.Entanglement entropy

    It is argued that vacuum entanglement energy associated with the entanglement entropy of the Universe can be viewed as the origin of DE [56].In the quantum field theory,the entanglement entropy of the vacuum with a horizon can be written as

    where TEnt=1/(2πRh) is the Gibbons–Hawking temperature.Integrating equation (20),one can get

    where Ndofis the number of light fields present in the vacuum.Thus the DE energy density is

    4.2.Holographic gas

    As is known,a system that appears nonperturbative may be described by weakly interacting quasi-particle excitations.Moreover,it is argued that the quasi-particle excitations of such a system may be described by a gas of holographic particles [58],with modified degeneracy

    where V is the volume of the system,w0,A,and B are dimensionless constants.Note that with the temperature T ∝V-1/3and the entropy S ∝V2/3,one can obtain the relationship B=(A+2)/3.Therefore,the corresponding energy density of the system is

    It is clear that this DE energy density has the same form as equation (8).

    4.3.Casimir energy

    As is well known,Casimir energy is a core prediction of quantum field theory [59–62].It is argued that the Casimir energy in a static de Sitter space may be viewed as the origin of DE [63,64].

    The Casimir energy satisfies

    Making use of the heat kernel method with ζ function regularization,It can be calculated as

    4.4.Entropic force

    In 2010,Verlinde conjectured that gravity may be essential an entropic force [65].Based on this idea,[66] suggested that the entropy change of the future event horizon should be considered together with the entropy change of the test holographic screen.

    Let us consider a test particle with physical radial coordinate R.Based on Verlinde’s proposal,the energy associated with the future event horizon Rhsatisfies

    whereNh~is the number of degrees of freedom on the horizon,Th~1/Rhis the Gibbons–Hawking temperature.Note that the energy of the horizon induces a force to a test particle of order Fh~GEhm/R2,which can be integrated to obtain a potential

    Using the standard argument leading to Newtonian cosmology,this potential term will show up in the Friedmann equation as a DE componentρde=.Again,this energy density is the same as equation (8).

    4.5.Action principle

    Finally,we introduce how to derive the general formula of HDE from the action principle [67].

    Consider the action

    Since L(a →∞)=0,aL is just the future event horizon.Moreover,one can obtain the DE energy density

    In addition to the expression of equation (8),this DE energy density has a new termwhich can be interpreted as dark radiation [68].

    5.OHDE model with dark sector interaction

    The interaction between dark sectors is a hot topic in the field of DE [69].In this section,we introduce the research works about the OHDE model with dark sector interaction.

    5.1.Dynamical evolution

    Consider the OHDE model with dark sector interaction in a non-flat Universe,the first Friedmann equation is

    In addition,the energy density of DM and HDE satisfy

    where Q phenomenologically describes the interaction term.

    It should be mentioned that Q cannot be derived from the first principle,and the most common form of Q is

    where Γ1,Γ2are dimensionless constant parameters.For the specific form of Q,three choices are often made in the previous literature,i.e.Γ2=0,Γ1=0 and Γ1=Γ2=Γ3,which leads to three most common interaction form

    Based on the energy conservation equations for all the energy components in the Universe,we obtain,

    Substituting this expression of pdeinto equation (90),one can get

    which is a derivative equation ofandwhere

    In a non-flat Universe,L takes the form

    Note that equation (43) can give another derivative equation ofand

    Based on the equations (41) and (45),one can obtain

    These two equations describe the dynamical evolution of the IHDE model in a non-flat Universe.

    5.2.Equation of state

    Then,we discuss the EoS w of the IHDE model.For simplicity,we only consider the case of a flat Universe.Let us take into account the interaction between matter and HDE,then

    Consider the ratio of energy densities [73]

    Based on the equations (48) and (49),we can obtain

    It is clear that

    then we have

    It should be mentioned that,if DE decays into pressureless matter (i.e.Q >0),it will yield a more negative w.

    For the OHDE model,Equation (47) leads to

    Making use of the equations (54) and (53),one can obtain

    [73] considered a interaction form Q=3b2Hρc,then

    It should be mentioned that,if the following two conditions

    are satisfied,one can get w <-1.In other words,the IHDE model can accommodate a transition from a quintessence DE to a phantom DE.This conclusion holds true for the case of a Universe with spatial curvature [74].

    5.3.Alleviation of coincidence problem

    Now we discuss the coincidence problem under the frame of HDE.For the OHDE model without DM/DE interaction,equation (51) can be reduced to

    wherex≡ lna.For the case of constant w,we get

    One can see that r~O(1) only when t is around t0,so the coincidence problem still exists for this case.

    The inclusion of the DM/DE interaction can make a big difference.For example,[75] choosing Q=Γρde,then get

    In addition,by choosing the Hubble scale 1/H as the characteristic length scale L,one gets [75]

    Based on equations (61) and (62),one can obtain

    This means that the coincidence problem can be solved by appropriately choosing the interaction term Q and the characteristic length scale L.

    It should be mentioned that,for the case of the OHDE model,adding the DM/DE interaction alone cannot remove the coincidence problem completely.However,[76] demonstrated that for the IHDE model with an appropriate interacting term,setting ˙r=0 will give a positive solution of r that has a stable constant solution,whose value is close to the current measured value.Therefore,the inclusion of DM/DE interaction can ensure r varies with time slowly,thus greatly alleviating the coincidence problem [77–79].

    5.4.Generalized second law of thermodynamics

    It is believed that there is a deep connection between GR and thermodynamics [80–84].In the following,we will discuss the generalized second law of thermodynamics under the frame of the IHDE model.

    For an IHDE mode with an interaction term Q=Γρde,one can define the effective EoS

    The continuity equations satisfy

    Moreover,the entropy of the Universe inside the future event horizon takes the forms

    Note that the entropy of horizon is SL=πL2,so

    The validity of generalized second law of thermodynamics has been tested under the frame of the IHDE model.For example,by adopting the parameters Ωde0=0.73,Ωk0=0.01,C=0.1 and b2=0.2,Setare studied this topic and found that [85]

    6.Four types of holographic dark energy models

    All the sections above only focus on the OHDE model.In fact,there are four types of HDE models.

    To show the differences among the four types of HDE models,let us consider a universe that has DE and characteristic length scale L.As pointed out by Cohen et al [46],the energy density of this universe cannot exceed the energy density of a black hole.Therefore,the IR cutoff (characteristic length scale L) and UV cutoff (vacuum quantum zero point energy Λ) should satisfy

    where SBHis the black hole entropy.Making use of the Bekenstein formula of black hole entropy SBH∝A ∝L2,and noting that vacuum energy density ρde=Λ4,one can derive

    This is the core formula for HDE.

    As mentioned above,the simplest choice,i.e.the Hubble scale L=1/H,can not yield cosmic acceleration.In the past 20 years,a lot of HDE models have been proposed.These theoretical models can be divided into four categories: (1)HDE models with the other characteristic length scale;(2)HDE models with extended Hubble scale;(3) HDE models with dark sector interaction;(4) HDE models with modified black hole entropy.In this section,we will introduce these four types of HDE models.

    6.1.HDE models with other characteristic length scale

    This type of HDE model chooses the other characteristic length scale,which has nothing to do with the Hubble scale,as the IR cutoff.It is clear that the OHDE model belongs to this category.Another well-known HDE model of this category is the agegraphic dark energy (ADE) model.

    [86,87] suggested that one can choose the time of the Universe as the IR cutoff,which is the core idea of ADE model.

    The first version of ADE [86] adopted the physical time t as the IR cutoff.But this version of ADE model cannot evolve from a sub-dominate component to a dominate component.Soon after,a realistic model of ADE was proposed [87].It is suggested that one can adopt the conformal time of the Universe as the IR cutoff.In this new version,the energy density of ADE satisfies

    where η is the conformal time

    The fractional energy density is

    The evolution equation of Ωdeis

    In addition,the EoS of ADE is

    In a matter-dominated Universe,η∝Based on equation (75),one can get ρde∝1/a.Based on the continuity equation,one can get w=-2/3.Compare this result to equation (79)),one obtains that,

    It is clear that the fractional energy density of ADE in the matter-dominated era is determined.Therefore,there is no coincidence problem in the ADE model.

    For the studies of other HDE models of this category,see[88,89].

    6.2.HDE models with extended Hubble scale

    This type of HDE model chooses the combination of the Hubble scale and its time derivatives as the IR cutoff.

    A well-known HDE model of this category is the Ricci dark energy (RDE) model [90,91].In the FLRW cosmology,the Ricci scalar is

    Adopting the Ricci curvature as the IR cutoff,one can obtain the energy density of RDE

    Thus,the first Friedmann equation satisfies

    wherex≡ lna.This equation can be written as

    where f0is an integration constant,which can be fixed by using the condition E0=1:

    Based on equation (84),one can get

    In addition,the EoS of RDE satisfies

    If α=1/2,RDE will behave as a cosmological constant plus a DM.If 1/2 ≤α <1,RDE will behave as a quintessence DE.If α <1/2,RDE will start from a quintessence DE and evolve to a phantom DE.

    For the studies of other HDE models of this category,see[92–96].

    6.3.HDE models with dark sector interaction

    This type of HDE model chooses the Hubble scale as the IR cutoff,while the interaction between dark matter and dark energy is taken into account.

    In a non-flat Universe,the first Friedmann equation is

    After taking into account the interaction between dark sectors,the energy density of DM and HDE satisfy

    where Q describes the energy flow between dark matter and dark energy.

    If there is no energy flow between dark matter and dark energy,i.e.Q=0,choosing the Hubble scale as IR cutoff will give a wrong EoS of HDE,which yields a universe without cosmic acceleration.However,the introduction of dark sector interaction can change the dynamical evolution equation of HDE,as well as the EoS of HDE.Therefore,after adopting an appropriate form of Q,choosing the Hubble scale as the IR cutoff can also yield cosmic acceleration.

    For more details about the HDE models with dark sector interaction,see the review article [69] and the references therein.

    6.4.HDE Models with modified black hole entropy

    This type of HDE model chooses the Hubble scale as the IR cutoff,while the formula of black hole entropy is modified.The most popular HDE model in this category is the Tsallis holographic dark Energy (THDE) model.

    In [97],Tavayef et al proposed the THDE model.This model is based on a modified entropy area relation,which is suggested by Tsallis and Cirto [98],

    where δ is an unknown constant and γ is a non-additivity parameter.Based on the holographic principle,one can derive a relation among the system entropy S,the IR cutoff L and UV cutoff Λ [99]

    Combining equations (91) and (92),one can obtain

    Note that Λ4denotes the vacuum energy density.Based on this inequality,the energy density of THDE can be written as [97]

    where B is a constant model parameter.Moreover,[97]proved that,for a flat FLRW universe filled by THDE and pressureless matter,choosing the Hubble horizon as the IR cutoff will yield cosmic acceleration.

    In recent years,the THDE model has drawn a lot of attention [100–105].In addition to many theoretical explorations and observational constraints,this model has also been studied in various modified gravity theories,such as Brans Dicke theory [106] and Brane cosmology [107].

    It should be mentioned that there are some other theoretical attempts at the entropy-corrected HDE models,such as the Barrow holographic dark energy [108–110],the Renyi holographic dark energy [111,112] and the Kaniadakis holographic dark energy [113].For the studies of other HDE models of this category,see [114–117].

    7.Hubble tension problem and holographic dark energy

    In the recent years,the Hubble tension problem has become one of the biggest challenges of cosmology [118].In this section,we introduce the Hubble tension problem,as well as the attempts to alleviate this problem under the framework of HDE.

    7.1.Hubble tension problem

    Since the 21st century,it was widely believed that the simplest cosmological model,i.e.the ΛCDM model,is most favored by various astronomical observations.Therefore,the ΛCDM model was also called the standard model of cosmology.However,in recent years,it is found that under the framework of the ΛCDM model,the high redshift cosmic microwave background (CMB) observations and the low redshift cepheid observations will give very different measurement results of the Hubble constant H0.

    For example,under the framework of the ΛCDM model,the Planck 2018 data,which is the last release from the Planck satellite measurements of the CMB anisotropies,gave H0=67.4 ± 0.5 km s-1Mpc-1[119].On the other side,under the framework of the ΛCDM model,based on the analysis of cepheids in 42 Type Ia supernova host galaxies,Riess et al gave H0=73.04 ± 1.04 km s-1Mpc-1[120].It is clear that these two measurement results of H0have a very big tension.It must be emphasized that the difference between the H0measurement results given by these two observations has exceeded the 5σ confidence level (CL).In other words,the Hubble constant tension between the early time and late time measurements of the Universe has exceeded 5σ CL.

    Therefore,there is an impossible triangle among the high redshift CMB observations,the low redshift cepheid observations,and the ΛCDM model.In other words,at least one of the three factors is wrong.If not due to the systematic errors of the CMB and the cepheid observations,the Hubble constant tension will reveal an exciting possibility: what we need is new physics beyond the standard model of cosmology.

    7.2.Alleviation of Hubble tension problem under the framework of HDE

    A lot of theoretical attempts have been made to alleviate the Hubble tension problem [118],such as early dark energy[121,122],late dark energy [123,124],modified gravity[125,126],sterile neutrino [127] and dark sector interaction[128].In this review,we only focus on one kind of late dark energy,i.e.HDE.

    Some literature has discussed the possibility of alleviating the Hubble tension problem under the framework of the OHDE model.For example,[129] found that,after taking into account the OHDE model and sterile neutrino,the combined data of Planck 2015+BAO+JLA+R16 will give H0=70.7 ± 1.1 km s-1Mpc-1;for this case,the difference with low redshift cepheid observations is reduced by 1.5σ.In addition,[130] found that,based on the OHDE model,the combined data of Planck 2018+BAO+R19 gives H0=73.12 ± 1.14 km s-1Mpc-1,which has no tension with low redshift cepheid observations.

    In addition,the case of Tsallis holographic dark energy has also been studied.[131] found that,for this model,Planck 2018+BAO+BBN+CC+Pantheon gives H0=69.8 ±1.8 km s-1Mpc-1,which alleviates the Hubble tension at 1.5σ CL.

    These studies show that the HDE model has the potential to alleviate the Hubble tension problem.

    8.Summary

    As the most important principle of quantum gravity,HP has the great potential to solve the DE problem.In this paper,we reviewed previous theoretical attempts at applying the HP to the DE problem.

    Based on the HP and the dimensional analysis,we gave the general formula of HDE energy density,i.e.ρde=Then,we introduced the OHDE model,which chooses the future event horizon as the characteristic length scale.Next,we introduced various theoretical motivations that can lead to the general formula of HDE.Moreover,we introduced the research works about the IHDE models,which consider the interaction between dark sectors.Moreover,we introduce all four types of HDE models that originate from HP,including (1) HDE models with other characteristic length scale;(2) HDE models with extended Hubble scale;(3) HDE models with dark sector interaction;(4) HDE models with modified black hole entropy.Finally,we introduce the well-known Hubble tension problem,as well as the attempts to alleviate this problem under the framework of HDE.

    From the perspective of theory,the core formula of HDE is obtained by combining the HP and the dimensional analysis,instead of adding a DE term into the Lagrangian.Therefore,HDE remarkably differs from any other theory of DE.From the perspective of observation,HDE can fit various astronomical data well,and have the potential to alleviate the Hubble tension problem.These features make HDE a very competitive dark energy scenario.

    Recent theoretical developments show that spacetime itself may be emergent from the entanglement entropy [132,133].This discovery will bring new insight to the theoretical explorations of HDE,as well as the theoretical studies of applying the HP to cosmology [134,135].In addition,S.Nojiri et al proved that the holographic approach can be used to describe the early-time acceleration and the late-time acceleration of our Universe in a unified manner [136].For more details,see [137,138].

    Acknowledgments

    We are grateful to Prof.Yi Wang for helpful discussions.SW is supported by the Guangdong Province Science and Technology Innovation Program under Grant No.2020A1414040009.ML is supported by the National Natural Science Foundation of China under Grant No.11 275 247 and No.11 335 012.

    给我免费播放毛片高清在线观看| 最新美女视频免费是黄的| 啪啪无遮挡十八禁网站| 亚洲精品一区av在线观看| 欧美一级a爱片免费观看看 | 叶爱在线成人免费视频播放| 日韩精品中文字幕看吧| 欧美色视频一区免费| 婷婷六月久久综合丁香| 夜夜爽天天搞| 国产精品电影一区二区三区| 国产精品 国内视频| 少妇人妻一区二区三区视频| 超碰成人久久| 成人国语在线视频| 免费看a级黄色片| 久久精品亚洲精品国产色婷小说| 免费在线观看成人毛片| 国产精品久久久人人做人人爽| 欧洲精品卡2卡3卡4卡5卡区| 香蕉丝袜av| 搡老岳熟女国产| 国产精品亚洲一级av第二区| 日日夜夜操网爽| 精品熟女少妇八av免费久了| 深夜精品福利| 亚洲全国av大片| 国语自产精品视频在线第100页| 精品一区二区三区av网在线观看| 国产精品 欧美亚洲| 欧美色视频一区免费| 听说在线观看完整版免费高清| 神马国产精品三级电影在线观看 | 午夜a级毛片| 午夜福利高清视频| 免费观看精品视频网站| 午夜老司机福利片| 欧美日韩亚洲综合一区二区三区_| 久久亚洲精品不卡| 国产精品综合久久久久久久免费| 亚洲专区字幕在线| 午夜久久久久精精品| 热99re8久久精品国产| 男女视频在线观看网站免费 | 久久久久性生活片| 免费搜索国产男女视频| 亚洲熟妇中文字幕五十中出| 国产真人三级小视频在线观看| 久久国产精品影院| 黑人欧美特级aaaaaa片| 精品熟女少妇八av免费久了| 亚洲aⅴ乱码一区二区在线播放 | 午夜成年电影在线免费观看| 日韩高清综合在线| 国产精品日韩av在线免费观看| 亚洲美女视频黄频| 999久久久国产精品视频| netflix在线观看网站| 国产久久久一区二区三区| 国产真实乱freesex| videosex国产| 男人舔女人下体高潮全视频| 亚洲专区中文字幕在线| 在线a可以看的网站| 国产探花在线观看一区二区| 欧美极品一区二区三区四区| 成人av在线播放网站| 免费人成视频x8x8入口观看| 天堂√8在线中文| 啦啦啦免费观看视频1| 三级男女做爰猛烈吃奶摸视频| 午夜久久久久精精品| 午夜福利视频1000在线观看| 亚洲熟妇熟女久久| 亚洲av成人不卡在线观看播放网| 国产伦在线观看视频一区| 久久久精品国产亚洲av高清涩受| 国产精品精品国产色婷婷| 好男人电影高清在线观看| 9191精品国产免费久久| av片东京热男人的天堂| а√天堂www在线а√下载| 免费高清视频大片| 亚洲自拍偷在线| 日本黄色视频三级网站网址| 搞女人的毛片| xxx96com| 一级作爱视频免费观看| 欧美成人性av电影在线观看| 精品福利观看| 欧美3d第一页| 又大又爽又粗| 久久久久久久精品吃奶| 欧美一区二区精品小视频在线| 欧美日韩国产亚洲二区| 国产激情久久老熟女| 日本a在线网址| 久久久久久九九精品二区国产 | 国产黄a三级三级三级人| 国产精品香港三级国产av潘金莲| 嫩草影视91久久| av福利片在线观看| 亚洲av片天天在线观看| 两个人看的免费小视频| 日本在线视频免费播放| x7x7x7水蜜桃| 丝袜人妻中文字幕| 免费人成视频x8x8入口观看| 久久久久久大精品| 长腿黑丝高跟| 岛国视频午夜一区免费看| 国产一区在线观看成人免费| 国产成人系列免费观看| 日韩精品免费视频一区二区三区| 熟女电影av网| 日本熟妇午夜| 99精品在免费线老司机午夜| 一卡2卡三卡四卡精品乱码亚洲| 日本一区二区免费在线视频| 久久性视频一级片| 国产伦人伦偷精品视频| 一二三四社区在线视频社区8| 美女大奶头视频| ponron亚洲| 久久香蕉精品热| av福利片在线观看| 一本综合久久免费| 精品国产乱子伦一区二区三区| 一本精品99久久精品77| 欧美丝袜亚洲另类 | 欧美最黄视频在线播放免费| 亚洲国产中文字幕在线视频| 欧美色欧美亚洲另类二区| 亚洲五月婷婷丁香| 亚洲一码二码三码区别大吗| 精品久久久久久久毛片微露脸| 欧美黑人欧美精品刺激| 亚洲欧美日韩无卡精品| 一级毛片精品| 国产亚洲av嫩草精品影院| 亚洲成人精品中文字幕电影| 成人精品一区二区免费| 精品无人区乱码1区二区| 亚洲熟妇熟女久久| 久久香蕉精品热| 男男h啪啪无遮挡| 中文字幕久久专区| 亚洲欧美日韩高清在线视频| 精品国产乱子伦一区二区三区| 制服诱惑二区| 人人妻人人澡欧美一区二区| 欧美丝袜亚洲另类 | 久久香蕉精品热| 婷婷精品国产亚洲av| 757午夜福利合集在线观看| 欧美乱码精品一区二区三区| 成人18禁高潮啪啪吃奶动态图| 蜜桃久久精品国产亚洲av| www国产在线视频色| 免费在线观看亚洲国产| 一边摸一边抽搐一进一小说| 亚洲黑人精品在线| 亚洲性夜色夜夜综合| 久久天堂一区二区三区四区| avwww免费| 五月伊人婷婷丁香| 国产野战对白在线观看| 男人舔女人的私密视频| 亚洲真实伦在线观看| 又粗又爽又猛毛片免费看| 天天躁夜夜躁狠狠躁躁| 999久久久国产精品视频| 99国产极品粉嫩在线观看| 国产av一区在线观看免费| 99久久综合精品五月天人人| 亚洲免费av在线视频| 国产97色在线日韩免费| 精品一区二区三区四区五区乱码| xxxwww97欧美| 特大巨黑吊av在线直播| 高清在线国产一区| xxx96com| 久久久久国产一级毛片高清牌| 午夜福利视频1000在线观看| 丝袜人妻中文字幕| 禁无遮挡网站| 国产麻豆成人av免费视频| 国产熟女午夜一区二区三区| 这个男人来自地球电影免费观看| 久久精品成人免费网站| 久久精品成人免费网站| a在线观看视频网站| 男人的好看免费观看在线视频 | 91九色精品人成在线观看| 精品久久久久久久人妻蜜臀av| 久久精品国产综合久久久| 99精品在免费线老司机午夜| 中文字幕高清在线视频| 精品少妇一区二区三区视频日本电影| 亚洲国产高清在线一区二区三| 香蕉久久夜色| 久久久久久亚洲精品国产蜜桃av| 长腿黑丝高跟| 日韩欧美国产一区二区入口| 特级一级黄色大片| 亚洲成a人片在线一区二区| 亚洲av第一区精品v没综合| 亚洲片人在线观看| 欧美精品亚洲一区二区| 久久午夜综合久久蜜桃| 亚洲一卡2卡3卡4卡5卡精品中文| 久久精品国产清高在天天线| 国产午夜福利久久久久久| 久久久精品大字幕| 亚洲成人久久爱视频| 亚洲一码二码三码区别大吗| 日韩三级视频一区二区三区| 久久香蕉国产精品| av有码第一页| 91av网站免费观看| 国模一区二区三区四区视频 | 国产三级黄色录像| 久久中文字幕人妻熟女| 久久久久久久精品吃奶| 男插女下体视频免费在线播放| 欧美成人一区二区免费高清观看 | 美女 人体艺术 gogo| 午夜精品一区二区三区免费看| 老司机靠b影院| 亚洲精品美女久久久久99蜜臀| 夜夜爽天天搞| 亚洲第一电影网av| 看免费av毛片| 国产成人av教育| 成人三级黄色视频| 大型av网站在线播放| 夜夜夜夜夜久久久久| 免费观看人在逋| or卡值多少钱| cao死你这个sao货| 真人一进一出gif抽搐免费| 两人在一起打扑克的视频| e午夜精品久久久久久久| 熟女少妇亚洲综合色aaa.| 啦啦啦韩国在线观看视频| 免费在线观看日本一区| 黄色毛片三级朝国网站| 亚洲一区中文字幕在线| 两个人的视频大全免费| 亚洲精品一区av在线观看| 在线永久观看黄色视频| 19禁男女啪啪无遮挡网站| 国产精品 国内视频| 这个男人来自地球电影免费观看| 1024手机看黄色片| 可以免费在线观看a视频的电影网站| 亚洲第一电影网av| 啦啦啦韩国在线观看视频| 国语自产精品视频在线第100页| 91字幕亚洲| 99久久精品热视频| 国产精品爽爽va在线观看网站| 夜夜爽天天搞| 国产成人aa在线观看| www.精华液| 9191精品国产免费久久| 国产精品1区2区在线观看.| 我的老师免费观看完整版| 亚洲欧美日韩高清在线视频| 欧美日韩黄片免| 欧美日韩中文字幕国产精品一区二区三区| 成年女人毛片免费观看观看9| 久热爱精品视频在线9| 亚洲熟妇熟女久久| 亚洲成a人片在线一区二区| 又黄又爽又免费观看的视频| 欧美午夜高清在线| 香蕉国产在线看| 国产成人精品久久二区二区免费| 一级a爱片免费观看的视频| 桃红色精品国产亚洲av| 色综合婷婷激情| 一区福利在线观看| 好男人在线观看高清免费视频| 熟妇人妻久久中文字幕3abv| 国产在线观看jvid| 久久久久久大精品| 高清毛片免费观看视频网站| 久久久久性生活片| 久久人妻av系列| 亚洲国产欧美网| 亚洲中文字幕一区二区三区有码在线看 | 亚洲狠狠婷婷综合久久图片| 香蕉丝袜av| 亚洲一卡2卡3卡4卡5卡精品中文| 色尼玛亚洲综合影院| 欧美日本视频| 一二三四在线观看免费中文在| www.自偷自拍.com| 国产免费av片在线观看野外av| 露出奶头的视频| 日本一二三区视频观看| 夜夜躁狠狠躁天天躁| 777久久人妻少妇嫩草av网站| 每晚都被弄得嗷嗷叫到高潮| 午夜免费成人在线视频| 国产av一区二区精品久久| 久久精品综合一区二区三区| 亚洲五月天丁香| 久99久视频精品免费| 国产精品 欧美亚洲| 两性午夜刺激爽爽歪歪视频在线观看 | 男人舔奶头视频| 免费av毛片视频| 叶爱在线成人免费视频播放| 亚洲成人久久爱视频| 九色国产91popny在线| 免费无遮挡裸体视频| 天天躁狠狠躁夜夜躁狠狠躁| 亚洲av成人av| 欧美乱妇无乱码| 久久人妻av系列| 国产精品免费视频内射| 亚洲精品一区av在线观看| 国产精品九九99| 这个男人来自地球电影免费观看| 精品日产1卡2卡| 波多野结衣巨乳人妻| 午夜福利高清视频| 18禁国产床啪视频网站| 亚洲性夜色夜夜综合| 亚洲成人久久爱视频| 精品国产乱子伦一区二区三区| 中文亚洲av片在线观看爽| 久久这里只有精品中国| 国产亚洲精品久久久久5区| 在线看三级毛片| 日韩欧美在线乱码| 亚洲全国av大片| 19禁男女啪啪无遮挡网站| 日本 欧美在线| 黄色丝袜av网址大全| 欧美 亚洲 国产 日韩一| 国产男靠女视频免费网站| 淫秽高清视频在线观看| 在线观看日韩欧美| 欧美最黄视频在线播放免费| 国产高清视频在线播放一区| 日韩三级视频一区二区三区| 给我免费播放毛片高清在线观看| 在线播放国产精品三级| 亚洲国产精品合色在线| av欧美777| 狠狠狠狠99中文字幕| 特大巨黑吊av在线直播| 一级黄色大片毛片| 91字幕亚洲| 国产欧美日韩精品亚洲av| 国产精品久久视频播放| 欧美极品一区二区三区四区| 成人永久免费在线观看视频| 国产av在哪里看| 亚洲九九香蕉| 99久久精品国产亚洲精品| 人妻丰满熟妇av一区二区三区| 亚洲va日本ⅴa欧美va伊人久久| 日韩欧美国产一区二区入口| 国产高清视频在线观看网站| 免费看十八禁软件| www.熟女人妻精品国产| 亚洲专区字幕在线| 国产三级在线视频| 亚洲狠狠婷婷综合久久图片| 欧美色欧美亚洲另类二区| 午夜精品一区二区三区免费看| 在线观看www视频免费| 亚洲片人在线观看| 18美女黄网站色大片免费观看| 日本三级黄在线观看| 少妇熟女aⅴ在线视频| av欧美777| 啪啪无遮挡十八禁网站| 色av中文字幕| 曰老女人黄片| 免费av毛片视频| 日本一二三区视频观看| 观看免费一级毛片| 国产视频一区二区在线看| 国产欧美日韩精品亚洲av| 99在线视频只有这里精品首页| 国产aⅴ精品一区二区三区波| 又黄又爽又免费观看的视频| 2021天堂中文幕一二区在线观| 一进一出抽搐gif免费好疼| 国产欧美日韩一区二区三| 十八禁人妻一区二区| 国产aⅴ精品一区二区三区波| 亚洲中文字幕一区二区三区有码在线看 | 久久国产精品人妻蜜桃| 麻豆成人av在线观看| 国产精品一及| 久久性视频一级片| 亚洲欧美日韩高清在线视频| 日韩欧美国产一区二区入口| 国产伦人伦偷精品视频| 久久久久国产一级毛片高清牌| 亚洲国产精品合色在线| 日韩 欧美 亚洲 中文字幕| 日本免费a在线| 久久久久性生活片| 国产精品亚洲美女久久久| 99re在线观看精品视频| 18美女黄网站色大片免费观看| 国产精品 欧美亚洲| 欧美日韩精品网址| 1024香蕉在线观看| 高清毛片免费观看视频网站| 日日摸夜夜添夜夜添小说| 午夜免费成人在线视频| 久久久久久久精品吃奶| 国产在线精品亚洲第一网站| 午夜视频精品福利| 国产精品av久久久久免费| 欧美成人免费av一区二区三区| 777久久人妻少妇嫩草av网站| 国产精品免费一区二区三区在线| 国产成人影院久久av| 99久久99久久久精品蜜桃| 久久久久亚洲av毛片大全| 我要搜黄色片| 欧美日韩亚洲国产一区二区在线观看| 变态另类成人亚洲欧美熟女| 在线免费观看的www视频| 久99久视频精品免费| 又黄又粗又硬又大视频| 色噜噜av男人的天堂激情| 久久久久国内视频| 欧美最黄视频在线播放免费| 成人国产综合亚洲| 国产三级在线视频| 一夜夜www| 真人一进一出gif抽搐免费| 人妻丰满熟妇av一区二区三区| 嫩草影视91久久| а√天堂www在线а√下载| 国产高清videossex| 午夜福利高清视频| 亚洲av第一区精品v没综合| 国产高清videossex| 成人特级黄色片久久久久久久| 嫩草影院精品99| 一卡2卡三卡四卡精品乱码亚洲| 国产视频一区二区在线看| 久久久久久大精品| www国产在线视频色| 黑人巨大精品欧美一区二区mp4| 久久久久久久午夜电影| 精品午夜福利视频在线观看一区| 最近最新免费中文字幕在线| 久久久久久久午夜电影| 老司机午夜福利在线观看视频| 777久久人妻少妇嫩草av网站| 国产精品免费一区二区三区在线| aaaaa片日本免费| 国产精品99久久99久久久不卡| 国产黄a三级三级三级人| 99久久综合精品五月天人人| 精品一区二区三区视频在线观看免费| 90打野战视频偷拍视频| 欧美中文综合在线视频| 亚洲精品中文字幕在线视频| 香蕉丝袜av| 一本精品99久久精品77| 人人妻,人人澡人人爽秒播| 国产成人精品久久二区二区91| 国产成人av激情在线播放| 亚洲自拍偷在线| 亚洲精品久久国产高清桃花| 可以在线观看毛片的网站| 巨乳人妻的诱惑在线观看| 成年人黄色毛片网站| 国产成+人综合+亚洲专区| 国产私拍福利视频在线观看| 国产成人av教育| 国产精品1区2区在线观看.| 久久精品综合一区二区三区| 欧洲精品卡2卡3卡4卡5卡区| 午夜视频精品福利| 国产精品久久久久久人妻精品电影| 久久久精品大字幕| 少妇人妻一区二区三区视频| 俺也久久电影网| 无限看片的www在线观看| 国产一区二区在线av高清观看| 色综合欧美亚洲国产小说| 亚洲 国产 在线| 国产精华一区二区三区| 成人国产综合亚洲| 黄色视频,在线免费观看| 久久久精品大字幕| 久久亚洲精品不卡| 亚洲人成伊人成综合网2020| 成人特级黄色片久久久久久久| 91av网站免费观看| 两个人看的免费小视频| 午夜a级毛片| 亚洲人成伊人成综合网2020| 在线观看免费视频日本深夜| 国产伦人伦偷精品视频| 亚洲中文日韩欧美视频| 亚洲男人天堂网一区| 亚洲欧美精品综合久久99| 嫩草影视91久久| 青草久久国产| 亚洲午夜精品一区,二区,三区| 九九热线精品视视频播放| 成人18禁高潮啪啪吃奶动态图| 国产一区二区在线观看日韩 | 97超级碰碰碰精品色视频在线观看| 亚洲电影在线观看av| a级毛片在线看网站| 亚洲最大成人中文| 成人高潮视频无遮挡免费网站| 国产欧美日韩精品亚洲av| 国产久久久一区二区三区| 久久国产乱子伦精品免费另类| 好男人在线观看高清免费视频| 国产精品一区二区精品视频观看| 叶爱在线成人免费视频播放| 丁香六月欧美| 欧美黑人欧美精品刺激| 色尼玛亚洲综合影院| 亚洲成人中文字幕在线播放| 老司机午夜十八禁免费视频| 少妇粗大呻吟视频| 1024手机看黄色片| 国产精品99久久99久久久不卡| 舔av片在线| svipshipincom国产片| 午夜视频精品福利| 亚洲av第一区精品v没综合| 成人18禁在线播放| 亚洲成人免费电影在线观看| 久久精品影院6| 免费看日本二区| 午夜两性在线视频| 19禁男女啪啪无遮挡网站| 中出人妻视频一区二区| 人人妻人人澡欧美一区二区| 制服诱惑二区| 亚洲熟女毛片儿| av超薄肉色丝袜交足视频| 欧美激情久久久久久爽电影| 少妇裸体淫交视频免费看高清 | 国产午夜福利久久久久久| 色精品久久人妻99蜜桃| 色老头精品视频在线观看| 日本a在线网址| 搡老熟女国产l中国老女人| 色综合站精品国产| 亚洲欧美日韩高清在线视频| 精品乱码久久久久久99久播| 成人18禁在线播放| 国产主播在线观看一区二区| 老司机午夜福利在线观看视频| 亚洲国产精品sss在线观看| 欧美极品一区二区三区四区| 亚洲成人精品中文字幕电影| 好男人在线观看高清免费视频| 欧美成人午夜精品| a级毛片在线看网站| 欧美激情久久久久久爽电影| 性色av乱码一区二区三区2| 国产精品亚洲美女久久久| 亚洲人成77777在线视频| 91在线观看av| 国产精品爽爽va在线观看网站| 日日爽夜夜爽网站| 亚洲精品美女久久久久99蜜臀| 黄色丝袜av网址大全| 久久婷婷人人爽人人干人人爱| 亚洲av电影不卡..在线观看| 一级a爱片免费观看的视频| 精品欧美一区二区三区在线| 亚洲美女黄片视频| 久久久久久亚洲精品国产蜜桃av| 人人妻人人澡欧美一区二区| 97超级碰碰碰精品色视频在线观看| 日本五十路高清| 国产麻豆成人av免费视频| 国产爱豆传媒在线观看 | 国产精品一区二区三区四区免费观看 | 91字幕亚洲| 1024手机看黄色片| 国产99白浆流出| 国产亚洲av嫩草精品影院| 亚洲 欧美 日韩 在线 免费| 午夜免费激情av| 国产一级毛片七仙女欲春2| 后天国语完整版免费观看| 伊人久久大香线蕉亚洲五| 老司机午夜十八禁免费视频| 久久久国产欧美日韩av| 精品午夜福利视频在线观看一区| 国产一区二区在线观看日韩 | 精品少妇一区二区三区视频日本电影| a级毛片在线看网站| 一二三四在线观看免费中文在| 麻豆av在线久日| 动漫黄色视频在线观看| 别揉我奶头~嗯~啊~动态视频| 午夜视频精品福利| 久久久精品国产亚洲av高清涩受| 波多野结衣高清无吗| 亚洲免费av在线视频|