Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop q...Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop quantum cosmology. Assuming that the dark energy has a constant bulk viscosity, it is found that the bulk viscosity effects influence only the quintessence model case leading to the existence of a viscous late time attractor solution of de- Sitter type, whereas the quantum geometry effects influence the phantom model case where the big rip singularity is removed. Moreover, our results of the Hubble parameter as a function of the redshift are in good agreement with the more recent data.展开更多
The Einstein＇s genera/relativity is formulated in the Hamiltonian form for a spatia/ly Bat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obta...The Einstein＇s genera/relativity is formulated in the Hamiltonian form for a spatia/ly Bat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obtain the Wheeler-DeWitt equation. Solving the Wheeler-DeWitt equation and employing the de Broglie-Bohm interpretation to the wave function of the universe, we obtain a new version of spatia/ly fiat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufilcientlv small.展开更多
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more f...The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more features from full loop quantum gravity.The path integrals can be formulated in both timeless and deparameterized frameworks.It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other.Moreover,the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe,which coincide with those obtained in canonical theory.展开更多
The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the lo...The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.展开更多
We investigate the cosmological model of viscous modified Chaplygin gas （VMCG） in classical and loop quantum cosmology （LQC）. Firstly, we constrain its equation of state parameters in the framework of standard cos...We investigate the cosmological model of viscous modified Chaplygin gas （VMCG） in classical and loop quantum cosmology （LQC）. Firstly, we constrain its equation of state parameters in the framework of standard cosmology from Union 2.1 SNe Ia data. Then, we probe the dynamical stability of this model in a universe filled with VMCG and baryonic fluid in LQC background. It is found that the model is very suitable with （χ2/d.o.f = 0.974） and gives a good prediction of the current values of the deceleration parameter q0 =∈ （-0.60, -0.57） and the effective state parameter ωeff∈ （-0.76, -0.74） that is consistent with the recent observational data. The model can also predict the time crossing when （ρDE ≈ Pmatter） at z = 0.75 and can solve the coincidence problem. In LQC background, the Big Bang singularity found in classical cosmology ceases to exist and is replaced by a bounce when the Hubble parameter vanishes at ρtot≈ρc.展开更多
This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper su...This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.展开更多
We studied the dynamics of pre-inflation with generic potentials,namely V(φ)■^(4)φand V(φ)■(1+φ)^(2),in the context of loop quantum cosmology,where the initial singularity is resolved by a non-singular quantum b...We studied the dynamics of pre-inflation with generic potentials,namely V(φ)■^(4)φand V(φ)■(1+φ)^(2),in the context of loop quantum cosmology,where the initial singularity is resolved by a non-singular quantum bounce.Initially,the background evolution is dominated by either kinetic or potential energy at the quantum bounce.In the case of kinetic energy dominated evolution at the bounce,we found three generic phases,namely bouncing,transition,and slow-roll inflation.The first two regimes vanish in the case of potential energy dominated evolution;however,slow-roll inflation remains.Therefore,we found physically viable initial conditions of the inflaton field,which must have a minimum number of e-folds of 60 to be compatible with observations.Additionally,we analyzed the phase space diagram for the models under consideration;we found that all the trajectories of the inflaton field start from the bounce and move toward stable attractor points.展开更多
Recently,a de-Sitter epoch has been found in the new model of loop quantum cosmology,which is governed by the scalar constraint with both Euclidean and Lorentz terms.The singularity free bounce in the new LQC model an...Recently,a de-Sitter epoch has been found in the new model of loop quantum cosmology,which is governed by the scalar constraint with both Euclidean and Lorentz terms.The singularity free bounce in the new LQC model and the emergent cosmology constant strongly suggest that the effective stress-energy tensor induced by quantum corrections must violate the standard energy conditions.In this study,we perform an explicit calculation to analyze the behaviors of specific representative energy conditions,i.e.,average null,strong,and dominant energy conditions.We reveal that the average null energy condition is violated at all times,while the dominant energy condition is violated only at a period around the bounce point.The strong energy condition is violated not only at a period around the bounce point but also in the whole period from the bounce point to the classical phase corresponding to the de Sitter period.Our results will shed some light on the construction of a wormhole and time machine,which usually require exotic matter to violate energy conditions.展开更多
In this paper,we study the dynamics of k-essence in loop quantum cosmology(LQC).The study indicates that the loop quantum gravity(LQG)effect plays a key role only in the early epoch of the universe and is diluted in t...In this paper,we study the dynamics of k-essence in loop quantum cosmology(LQC).The study indicates that the loop quantum gravity(LQG)effect plays a key role only in the early epoch of the universe and is diluted in the later stages.The fixed points in LQC are basically consistent with those in standard Friedmann-Robertson-Walker(FRW)cosmology.For most of the attractor solutions,the stability conditions in L Q C are in agreement with those for the standard FRW universe.For some special fixed points,however,tighter constraints are imposed thanks to the LQG effect.展开更多
Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calc...Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.展开更多
This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the...This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the Tatum and Seshavatharam Hubble temperature formulae can be derived using the Stephan-Boltzmann dispersion law. Thus, as explained herein, the era of high precision Planck scale quantum cosmology has arrived.展开更多
We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ = Γ_0(where Γ_0 is a constant) in "intermediate" in...We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ = Γ_0(where Γ_0 is a constant) in "intermediate" inflation and Γ = V(φ),(where V(φ) is the potential of tachyonic field) in "logamediate" inflation. We have assumed slow-roll condition to construct scalar field φ, potential V, N-folds, etc. Various slow-roll parameters have also been obtained.We have analyzed the stability of this model through graphical representations.展开更多
We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckion...We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G<sup>-1</sup>, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.展开更多
Using the synchronous coordinates,the creation of a Schwarzschild black hole immersed in a de Sitter spacetime can be viewed as a coherent creation of a collection of timelike geodesics.The previously supposed conical...Using the synchronous coordinates,the creation of a Schwarzschild black hole immersed in a de Sitter spacetime can be viewed as a coherent creation of a collection of timelike geodesics.The previously supposed conical singularities do not exist at the horizons of the constrained instanton.Instead,the unavoidable irregularity is presented as a nonvanishing second fundamental form elsewhere at the quantum transition 3-surface.The same arguments can be applied to charged,topological,or higher dimensional black hole cases.展开更多
This paper integrates a quantum conception of the Planck epoch early universe with FSC model formulae and the holographic principle, to offer a reasonable explanation and solution of the cosmological constant problem....This paper integrates a quantum conception of the Planck epoch early universe with FSC model formulae and the holographic principle, to offer a reasonable explanation and solution of the cosmological constant problem. Such a solution does not appear to be achievable in cosmological models which do not integrate black hole formulae with quantum formulae such as the Stephan-Boltzmann law. As demonstrated herein, assuming a constant value of Lambda over the great span of cosmic time appears to have been a mistake. It appears that Einstein’s assumption of a constant, in terms of vacuum energy density, was not only a mistake for a statically-balanced universe, but also a mistake for a dynamically-expanding universe.展开更多
We present how the Bekenstein-Hawking entropy of a growing black hole variant of R_(h)=ct cosmology model can be re-written as a function of the Cosmic Microwave Background(CMB)radiation temperature or Hubble paramete...We present how the Bekenstein-Hawking entropy of a growing black hole variant of R_(h)=ct cosmology model can be re-written as a function of the Cosmic Microwave Background(CMB)radiation temperature or Hubble parameter,rather than the Hubble radius,as first pointed out by Tatum and Seshavatharam[1].We then show how our CMB temperature formulae lead to much higher precision in the estimated entropy of the Hubble radius universe,since the CMB temperature can be measured with great precision.We also briefly discuss how the Schwarzschild metric can be re-written as a function of the Bekenstein-Hawking entropy,and how the entropy of the universe can be directly linked to recent estimates of the number of quantum operations in the universe since its beginning.展开更多
基金Supported by the Algerian Ministry of Education and ResearchDGRSDT
文摘Dynamical behaviors and stability properties of a flat space Friedmann-Robertson-Walker universe filled with pressureless dark matter and viscous dark energy are studied in the context of standard classical and loop quantum cosmology. Assuming that the dark energy has a constant bulk viscosity, it is found that the bulk viscosity effects influence only the quintessence model case leading to the existence of a viscous late time attractor solution of de- Sitter type, whereas the quantum geometry effects influence the phantom model case where the big rip singularity is removed. Moreover, our results of the Hubble parameter as a function of the redshift are in good agreement with the more recent data.
文摘The Einstein＇s genera/relativity is formulated in the Hamiltonian form for a spatia/ly Bat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obtain the Wheeler-DeWitt equation. Solving the Wheeler-DeWitt equation and employing the de Broglie-Bohm interpretation to the wave function of the universe, we obtain a new version of spatia/ly fiat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufilcientlv small.
基金Supported by National Natural Science Foundation of China under Grant No. 10975017the Fundamental Research Funds for the Central Universities
文摘The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more features from full loop quantum gravity.The path integrals can be formulated in both timeless and deparameterized frameworks.It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other.Moreover,the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe,which coincide with those obtained in canonical theory.
基金Supported by the National Natural Science Foundation of China under Grant No. 11175019the Fundamental Research Funds for the Central Universities
文摘The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.
基金Supported by the Algerian Ministry of Education and Research and DGRSDT
文摘We investigate the cosmological model of viscous modified Chaplygin gas （VMCG） in classical and loop quantum cosmology （LQC）. Firstly, we constrain its equation of state parameters in the framework of standard cosmology from Union 2.1 SNe Ia data. Then, we probe the dynamical stability of this model in a universe filled with VMCG and baryonic fluid in LQC background. It is found that the model is very suitable with （χ2/d.o.f = 0.974） and gives a good prediction of the current values of the deceleration parameter q0 =∈ （-0.60, -0.57） and the effective state parameter ωeff∈ （-0.76, -0.74） that is consistent with the recent observational data. The model can also predict the time crossing when （ρDE ≈ Pmatter） at z = 0.75 and can solve the coincidence problem. In LQC background, the Big Bang singularity found in classical cosmology ceases to exist and is replaced by a bounce when the Hubble parameter vanishes at ρtot≈ρc.
文摘This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.
文摘We studied the dynamics of pre-inflation with generic potentials,namely V(φ)■^(4)φand V(φ)■(1+φ)^(2),in the context of loop quantum cosmology,where the initial singularity is resolved by a non-singular quantum bounce.Initially,the background evolution is dominated by either kinetic or potential energy at the quantum bounce.In the case of kinetic energy dominated evolution at the bounce,we found three generic phases,namely bouncing,transition,and slow-roll inflation.The first two regimes vanish in the case of potential energy dominated evolution;however,slow-roll inflation remains.Therefore,we found physically viable initial conditions of the inflaton field,which must have a minimum number of e-folds of 60 to be compatible with observations.Additionally,we analyzed the phase space diagram for the models under consideration;we found that all the trajectories of the inflaton field start from the bounce and move toward stable attractor points.
基金Supported by the National Natural Science Foundation of China(NSFC)(11775082,12047519,11875006,11961131013)China Postdoctoral Science Foundation(2021M691072)。
文摘Recently,a de-Sitter epoch has been found in the new model of loop quantum cosmology,which is governed by the scalar constraint with both Euclidean and Lorentz terms.The singularity free bounce in the new LQC model and the emergent cosmology constant strongly suggest that the effective stress-energy tensor induced by quantum corrections must violate the standard energy conditions.In this study,we perform an explicit calculation to analyze the behaviors of specific representative energy conditions,i.e.,average null,strong,and dominant energy conditions.We reveal that the average null energy condition is violated at all times,while the dominant energy condition is violated only at a period around the bounce point.The strong energy condition is violated not only at a period around the bounce point but also in the whole period from the bounce point to the classical phase corresponding to the de Sitter period.Our results will shed some light on the construction of a wormhole and time machine,which usually require exotic matter to violate energy conditions.
基金Supported by the Natural Science Foundation of China(11775036)Fok Ying Tung Education Foundation(171006)Jian-Pin Wu is also supported by Top Talent Support Program from Yangzhou University.
文摘In this paper,we study the dynamics of k-essence in loop quantum cosmology(LQC).The study indicates that the loop quantum gravity(LQG)effect plays a key role only in the early epoch of the universe and is diluted in the later stages.The fixed points in LQC are basically consistent with those in standard Friedmann-Robertson-Walker(FRW)cosmology.For most of the attractor solutions,the stability conditions in L Q C are in agreement with those for the standard FRW universe.For some special fixed points,however,tighter constraints are imposed thanks to the LQG effect.
基金Project supported by the National Natural Science Foundation of China.
文摘Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.
文摘This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the Tatum and Seshavatharam Hubble temperature formulae can be derived using the Stephan-Boltzmann dispersion law. Thus, as explained herein, the era of high precision Planck scale quantum cosmology has arrived.
文摘We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ = Γ_0(where Γ_0 is a constant) in "intermediate" inflation and Γ = V(φ),(where V(φ) is the potential of tachyonic field) in "logamediate" inflation. We have assumed slow-roll condition to construct scalar field φ, potential V, N-folds, etc. Various slow-roll parameters have also been obtained.We have analyzed the stability of this model through graphical representations.
文摘We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G<sup>-1</sup>, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.
文摘Using the synchronous coordinates,the creation of a Schwarzschild black hole immersed in a de Sitter spacetime can be viewed as a coherent creation of a collection of timelike geodesics.The previously supposed conical singularities do not exist at the horizons of the constrained instanton.Instead,the unavoidable irregularity is presented as a nonvanishing second fundamental form elsewhere at the quantum transition 3-surface.The same arguments can be applied to charged,topological,or higher dimensional black hole cases.
文摘This paper integrates a quantum conception of the Planck epoch early universe with FSC model formulae and the holographic principle, to offer a reasonable explanation and solution of the cosmological constant problem. Such a solution does not appear to be achievable in cosmological models which do not integrate black hole formulae with quantum formulae such as the Stephan-Boltzmann law. As demonstrated herein, assuming a constant value of Lambda over the great span of cosmic time appears to have been a mistake. It appears that Einstein’s assumption of a constant, in terms of vacuum energy density, was not only a mistake for a statically-balanced universe, but also a mistake for a dynamically-expanding universe.
文摘We present how the Bekenstein-Hawking entropy of a growing black hole variant of R_(h)=ct cosmology model can be re-written as a function of the Cosmic Microwave Background(CMB)radiation temperature or Hubble parameter,rather than the Hubble radius,as first pointed out by Tatum and Seshavatharam[1].We then show how our CMB temperature formulae lead to much higher precision in the estimated entropy of the Hubble radius universe,since the CMB temperature can be measured with great precision.We also briefly discuss how the Schwarzschild metric can be re-written as a function of the Bekenstein-Hawking entropy,and how the entropy of the universe can be directly linked to recent estimates of the number of quantum operations in the universe since its beginning.
