状态方程穿越-1的暗能量模型
摘要
近年来许多超新星、宇宙微波背景辐射和宇宙大尺度结构等的天文观测结果均指出宇宙正在加速膨胀，而非原先传统理论所预测的减速膨胀。此一结论违反了我们对物质的认识(我们认为物质均受万有引力作用，而引力致使两物体永远是相互吸引的)，显示宇宙中必定存在一种具有负压强并且能起斥力作用的能量存在，称为“暗能量”，研究表明暗能量大约占据了现今宇宙总能量密度的三分之二，其本质与行为决定了我们宇宙的命运。因此它可说是目前宇宙学上最热门的研究课题之一。
暗能量究竟是什么?我们还不知道。只知道暗能量必须具备足够大的负压强，这样它所产生的斥力方能致使宇宙加速膨胀。而且现在我们在星系及星系团的范围内都无法探测到此能量的存在，所以暗能量近乎均匀的，至少在可探测尺度上是均匀的，而且与光子是没有相互作用的。
理论家们根据以上几点性质和来源于天文观测的限制，提出了很多暗能量模型，最简单的候选者是宇宙学常数，还有动力学暗能量模型如慢速滚动的标量场Quintessence，Phantom和Quintom等。这些模型的不同也表现在其状态方程ω_(de)=p_(de)/ρ_(de)的不同上，如：宇宙学常数对应于ω_(de)=-1，Quintessence对应于-1＜ω_(de)＜-1/3，Phantom对应于ω_(de)＜-1而Quintom的状态方程穿越-1，即暗能量状态方程从过去的ω_(de)＞-1演化到现在的ω_(de)＜-1。这些模型在描述宇宙方面都表现出与天文观测不同程度上的一致。给定了大量的暗能量模型，选择最适合于宇宙观测的暗能量模型与探索暗能量的神秘属性，是现代宇宙学研究的重要课题之一。
本论文首先回顾了宇宙学的基础知识，从宇宙学原理到大爆炸宇宙学以及暴胀宇宙理论。在论文的第二章，论述了宇宙加速膨胀及暗能量存在的观测依据，主要来源于超新星和宇宙微波背景辐射的观测结果。接下来介绍了暗能量的众多候选者，重点介绍了暗能量状态方程穿越-1的观测结果及实现此结果的暗能量模型。这也是我们所做工作的主要出发点。
第三章讨论了广义的Quintom暗能量模型。在Quintom暗能量中代表正动能的Quintessence项和代表负动能的Phantom项具有相同的权重，在决定暗能量的演化上具有同等的地位。我们加进了一个自由参数改变了Quintessence和Phantom等权重的情况，而且多了一个自由度，这样能更好地描述宇宙的演化。
第四章提出了与具体机制无关的暗物质与暗能量的统一模型：P_(dm)+p_(de)=B(z)(ρ_(dm)+ρ_(de))。根据宇宙的演化历史我们给出了选取B(z)的约束条件。在此约束条件下我们给出B(z)的具体形式，其能很好地描述宇宙过去的演化，并且对宇宙未来的演化给出了预测。
第五章讨论了暗能量相变，假定宇宙中只有非相对论性物质和暗能量，并且这两个成分间没有相互作用力即各自满足自己的守恒方程。这样我们可以根据它们各自的守恒方程和暗能量状态方程的可能取值，给出暗能量密度比分及其密度本身的演化。为选取暗能量模型给出一些依据。结合现在流行的暗能量状态方程穿越-1的演化行为(暗能量从Quintessence相到Phantom相的相变)我们得到了暗能量密度是先减小再增大的。延用二次函数作为暗能量密度，我们分析了相变点的情况，也证明了相变的暗能量能很好地描述宇宙的演化。
理论源于天文观测，第六章根据新发布的超新星数据，用幂级数模拟暗能量密度给出了暗能量密度的可能演化，我们得到两种可能的演化趋势，为研究暗能量和探索暗能量神秘性提供一些线索。
综上所述，我们主要研究了状态方程穿越-1的暗能量模型，它们均实现了宇宙从早期的减速膨胀到近期的加速膨胀。但我们的研究还是远远不够的，我们至今仍无法回答暗能量究竟是什么的问题。以及暗能量的存在对早期宇宙的结构形成有什么影响，以及对今天天体的行为有没有影响。我们期望将来的工作能对这些问题给出合理的解答。
The recent cosmological observations strongly support that the expansion of the universespeeds up rather than slows down, obtained by studying type Ia supernova, cosmic microwavebackground and large scale structure. Theoreticians think the existence of the mysteriouscomponent with negative pressure called "dark energy" is certain, which violates the basicconcept of the gravitational effect (gravitation makes any two bodies interattraction forever).The research shows that dark energy comprises about 2/3 of the total energy density of theuniverse whose nature and evolution decide the destiny of the universe. This is why darkenergy is regarded as the one of the most important research subjects of the recent cosmology.
It is unknown that what is dark energy on earth. It is recognized that dark energyhas enough sufficient negative pressure to drive the accelerating expansion. Otherwise, darkenergy has been not detected on the scale of galaxies and galaxy clusters, so dark energyevenly distributes in the whole universe or on the observable scales at least and it has nointeraction with the photons.
On the base of the above characters and the astronomical observations, the theoreticianspromoted many models of dark energy. The simplest model is a cosmological constant. Thereare many more complex models proposed attempting to explain dark energy either as adynamic substance: slow-rolling scalar field for example Quintessence, Phantom and Quintomand so on. The difference of these candidates for dark energy is the size of the state equationω_(de)=p_(de)/ρ_(de) and for the cosmological constantω_(de)= -1, for quintessence -1＜ω_(de)＜-1/3,for phantomω_(de)＜-1 and for quintom the crossing -1, namely, the state equation of darkenergy being below-1 around the present epoch evolved fromω_(de)＜-1 in the past. Thesemodels show various degrees of consistency with the observational data in describing theevolution of the universe. Given the plethora of models, choosing the models of the best fitto the observational data and investigating the properties of this mysterious component isone of the most exciting problems of modern cosmology.
In this thesis, first the basic knowledge of cosmology is reviewed including cosmologicalprinciple, big-bang cosmology and inflationary cosmology. In chapter 2, the observationalevidences for the accelerating expansion of the universe and the existence of dark energy arediscussed: type Ia supernova and cosmic microwave background. Many candidates of darkenergy are introduced, but lay an emphasis on the observations for the state equation of dark energy crossing -1 and introduce several models of dark energy which can realize the stateequation of dark energy being below -1 around the present epoch evolved fromω_(de)＜-1 inthe past. This is also the basic of this thesis.
In chapter 3, a generalized Quintom dark energy is studied. In the model of Quintom darkenergy, the weights of the negative-kinetic scalar field (Phantom) and that of the normal scalarfield (Quintessence) are equal. So they influence the evolution of dark energy comparably.The model of the generalized Quintom dark energy is developed by adding a parameter g tochange the situation of their equal weight and to increase the degree of freedom, which canbetter describe the evolution of the university.
In chapter 4, a unified equation for dark energy and dark matter is presented: P_(dm)+P_(de)=B(z)(ρ_(dm)+ρ_(de)). In terms of the evolution of the universe, some constraints for B(z) areproposed. Based on the constraints, given a concrete form of function B(z), the past evolutionof the universe can be obtained which is in consistence with what is recognized and the futureevolution of the universe can be forecasted.
In chapter 5, the phase transition of dark energy is discussed. The change rate of thefractional density and the density of dark energy can be obtained from the conservationcondition which gives some foundations to choose the models of dark energy. Combining thestate equation of dark energyω_(de) crossing -1(which can be regarded as the phase transitionof dark energy from Quintessence phase to Phantom phase), the conclusion can be obtainedthat the density of dark energy first decreases to a minimum then increases. Taken the densityof dark energy to be a quadratic function, the cosmological parameters corresponding to thetransformation point are analyzed and the conclusions show that dark energy of the phasetransition accords with the evolution of the universe.
In chapter 6, the possible evolution of dark energy is analyzed by using the powerseries. The parameters are constrained from the newly released Gold sample of the supernovadataset. Two kinds of evolutional trend of dark energy are obtained. Expect the study cangive some clues in probing into the nature of dark energy.
In summary, the models of dark energy for the state equation crossing -1 are analyzedwhichrealize that the universe transited from deceleration to acceleration. But These workcan not answer what is dark energy on earth, what is the influence of dark energy on thestructure formation, etc. Expect that the future work can well answer these questions.
暗能量究竟是什么?我们还不知道。只知道暗能量必须具备足够大的负压强，这样它所产生的斥力方能致使宇宙加速膨胀。而且现在我们在星系及星系团的范围内都无法探测到此能量的存在，所以暗能量近乎均匀的，至少在可探测尺度上是均匀的，而且与光子是没有相互作用的。
理论家们根据以上几点性质和来源于天文观测的限制，提出了很多暗能量模型，最简单的候选者是宇宙学常数，还有动力学暗能量模型如慢速滚动的标量场Quintessence，Phantom和Quintom等。这些模型的不同也表现在其状态方程ω_(de)=p_(de)/ρ_(de)的不同上，如：宇宙学常数对应于ω_(de)=-1，Quintessence对应于-1＜ω_(de)＜-1/3，Phantom对应于ω_(de)＜-1而Quintom的状态方程穿越-1，即暗能量状态方程从过去的ω_(de)＞-1演化到现在的ω_(de)＜-1。这些模型在描述宇宙方面都表现出与天文观测不同程度上的一致。给定了大量的暗能量模型，选择最适合于宇宙观测的暗能量模型与探索暗能量的神秘属性，是现代宇宙学研究的重要课题之一。
本论文首先回顾了宇宙学的基础知识，从宇宙学原理到大爆炸宇宙学以及暴胀宇宙理论。在论文的第二章，论述了宇宙加速膨胀及暗能量存在的观测依据，主要来源于超新星和宇宙微波背景辐射的观测结果。接下来介绍了暗能量的众多候选者，重点介绍了暗能量状态方程穿越-1的观测结果及实现此结果的暗能量模型。这也是我们所做工作的主要出发点。
第三章讨论了广义的Quintom暗能量模型。在Quintom暗能量中代表正动能的Quintessence项和代表负动能的Phantom项具有相同的权重，在决定暗能量的演化上具有同等的地位。我们加进了一个自由参数改变了Quintessence和Phantom等权重的情况，而且多了一个自由度，这样能更好地描述宇宙的演化。
第四章提出了与具体机制无关的暗物质与暗能量的统一模型：P_(dm)+p_(de)=B(z)(ρ_(dm)+ρ_(de))。根据宇宙的演化历史我们给出了选取B(z)的约束条件。在此约束条件下我们给出B(z)的具体形式，其能很好地描述宇宙过去的演化，并且对宇宙未来的演化给出了预测。
第五章讨论了暗能量相变，假定宇宙中只有非相对论性物质和暗能量，并且这两个成分间没有相互作用力即各自满足自己的守恒方程。这样我们可以根据它们各自的守恒方程和暗能量状态方程的可能取值，给出暗能量密度比分及其密度本身的演化。为选取暗能量模型给出一些依据。结合现在流行的暗能量状态方程穿越-1的演化行为(暗能量从Quintessence相到Phantom相的相变)我们得到了暗能量密度是先减小再增大的。延用二次函数作为暗能量密度，我们分析了相变点的情况，也证明了相变的暗能量能很好地描述宇宙的演化。
理论源于天文观测，第六章根据新发布的超新星数据，用幂级数模拟暗能量密度给出了暗能量密度的可能演化，我们得到两种可能的演化趋势，为研究暗能量和探索暗能量神秘性提供一些线索。
综上所述，我们主要研究了状态方程穿越-1的暗能量模型，它们均实现了宇宙从早期的减速膨胀到近期的加速膨胀。但我们的研究还是远远不够的，我们至今仍无法回答暗能量究竟是什么的问题。以及暗能量的存在对早期宇宙的结构形成有什么影响，以及对今天天体的行为有没有影响。我们期望将来的工作能对这些问题给出合理的解答。
The recent cosmological observations strongly support that the expansion of the universespeeds up rather than slows down, obtained by studying type Ia supernova, cosmic microwavebackground and large scale structure. Theoreticians think the existence of the mysteriouscomponent with negative pressure called "dark energy" is certain, which violates the basicconcept of the gravitational effect (gravitation makes any two bodies interattraction forever).The research shows that dark energy comprises about 2/3 of the total energy density of theuniverse whose nature and evolution decide the destiny of the universe. This is why darkenergy is regarded as the one of the most important research subjects of the recent cosmology.
It is unknown that what is dark energy on earth. It is recognized that dark energyhas enough sufficient negative pressure to drive the accelerating expansion. Otherwise, darkenergy has been not detected on the scale of galaxies and galaxy clusters, so dark energyevenly distributes in the whole universe or on the observable scales at least and it has nointeraction with the photons.
On the base of the above characters and the astronomical observations, the theoreticianspromoted many models of dark energy. The simplest model is a cosmological constant. Thereare many more complex models proposed attempting to explain dark energy either as adynamic substance: slow-rolling scalar field for example Quintessence, Phantom and Quintomand so on. The difference of these candidates for dark energy is the size of the state equationω_(de)=p_(de)/ρ_(de) and for the cosmological constantω_(de)= -1, for quintessence -1＜ω_(de)＜-1/3,for phantomω_(de)＜-1 and for quintom the crossing -1, namely, the state equation of darkenergy being below-1 around the present epoch evolved fromω_(de)＜-1 in the past. Thesemodels show various degrees of consistency with the observational data in describing theevolution of the universe. Given the plethora of models, choosing the models of the best fitto the observational data and investigating the properties of this mysterious component isone of the most exciting problems of modern cosmology.
In this thesis, first the basic knowledge of cosmology is reviewed including cosmologicalprinciple, big-bang cosmology and inflationary cosmology. In chapter 2, the observationalevidences for the accelerating expansion of the universe and the existence of dark energy arediscussed: type Ia supernova and cosmic microwave background. Many candidates of darkenergy are introduced, but lay an emphasis on the observations for the state equation of dark energy crossing -1 and introduce several models of dark energy which can realize the stateequation of dark energy being below -1 around the present epoch evolved fromω_(de)＜-1 inthe past. This is also the basic of this thesis.
In chapter 3, a generalized Quintom dark energy is studied. In the model of Quintom darkenergy, the weights of the negative-kinetic scalar field (Phantom) and that of the normal scalarfield (Quintessence) are equal. So they influence the evolution of dark energy comparably.The model of the generalized Quintom dark energy is developed by adding a parameter g tochange the situation of their equal weight and to increase the degree of freedom, which canbetter describe the evolution of the university.
In chapter 4, a unified equation for dark energy and dark matter is presented: P_(dm)+P_(de)=B(z)(ρ_(dm)+ρ_(de)). In terms of the evolution of the universe, some constraints for B(z) areproposed. Based on the constraints, given a concrete form of function B(z), the past evolutionof the universe can be obtained which is in consistence with what is recognized and the futureevolution of the universe can be forecasted.
In chapter 5, the phase transition of dark energy is discussed. The change rate of thefractional density and the density of dark energy can be obtained from the conservationcondition which gives some foundations to choose the models of dark energy. Combining thestate equation of dark energyω_(de) crossing -1(which can be regarded as the phase transitionof dark energy from Quintessence phase to Phantom phase), the conclusion can be obtainedthat the density of dark energy first decreases to a minimum then increases. Taken the densityof dark energy to be a quadratic function, the cosmological parameters corresponding to thetransformation point are analyzed and the conclusions show that dark energy of the phasetransition accords with the evolution of the universe.
In chapter 6, the possible evolution of dark energy is analyzed by using the powerseries. The parameters are constrained from the newly released Gold sample of the supernovadataset. Two kinds of evolutional trend of dark energy are obtained. Expect the study cangive some clues in probing into the nature of dark energy.
In summary, the models of dark energy for the state equation crossing -1 are analyzedwhichrealize that the universe transited from deceleration to acceleration. But These workcan not answer what is dark energy on earth, what is the influence of dark energy on thestructure formation, etc. Expect that the future work can well answer these questions.
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