动力学暗能量模型的研究
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摘要
上世纪80年代初暴涨理论的提出宣告了粒子宇宙学的诞生,而1998年暗能量的发现使粒子宇宙学成为了当今最热的物理学研究领域之一.从上世纪90年代以来,包括COBE和WMAP在内的各种宇宙学实验精确地测量了各个宇宙学参数,同时成功检验了暴涨等宇宙学理论,标志着精测宇宙学时代的到来.
在进入动力学暗能量模型这个主题之前,本文先介绍必要的宇宙学背景知识.广义相对论的时空观和动力学方程对理解现代宇宙学是不可或缺的,我们把这方而的简单介绍列于附录中.关于背景宇宙学,我们先引入满足宇宙学原理的最一般的度规,即Robertson-Walker度规,再根据爱因斯坦方程推出在这个度规下的动力学方程,然后考察给定状态方程的理想流体的动力学演化.接着,我们介绍粒子物理的基本知识,包括标准模型和超出标准模型,因为现代宇宙学也离不开粒子物理.之后,我们考察宇宙的热历史,即标准热大爆炸模型,分别列举了在辐射,物质以及暗能量为主时期发生的各个重要事件.鉴于与暗能量的相似性,这部分最后介绍对热大爆炸模型的一个重要修正,即原初暴涨模型.
我们接下来讨论暗能量的各种模型.这部分先介绍宇宙学常数模型,并指出它的两个问题,即精细调节问题和巧合性问题.基于这两个问题以及粒子物理理论方面的考虑和观测数据的现状,我们引入动力学暗能量模型,并考察了几种主要的动力学暗能量模型的基本思想,包括Quintessence,Phantom,Quintom,K-essence和全息暗能量.
之后,我们把注意力集中于Quintessence动力学暗能量模型.根据本论文对精细调节问题和巧合性问题的定义,引入动力学暗能量本身已经避免了精细调节问题,所以这部分主要探讨Quintessence的动力学演化怎样缓解巧合性问题.我们先简单介绍分析Quintessence的演化所需的自治动力学系统的知识.在化简Quintessence动力学系统之后,我们着重讨论两类模型:Tracking解和Scaling解.然后,我们考察与物质耦合的Quintessence模型对巧合性问题的启示.
最后我们进入本论文的创新性工作部分.这部分我们先引入一种新的重建Quintessence势的方法.用这种方法,我们很容易地得到一个以前没有发现的Tracker解,并很直接地得到一个多重吸引子解,即,在给定参数下有多于一个吸引子的解.然后,我们提出一个新的Quintessence模型.在这个模型中,Quintessence场,通过其场值在很短时间内的变化,从一个Scaling吸引子跳到一个类de Sitter吸引子使宇宙加速膨胀.我们接着计算了这样的跳跃所需的场值变化,并提出一个基于自发对称破缺的机制,来实现这个场值的突变.
The proposing of inflation theory in the early 1980s suggested the birth of particle cosmology, while the discovery of dark energy in 1998 has made it one of the hottest research areas in physics. On the other hand, various experiments in cosmology since the early 1990s, including COBE and WMAP, have measured cosmological parameters to high precision and been found to be in good agreement with cosmological theories like inflation, pronouncing the coming of the era of precision cosmology.
Before going into dynamical dark energy models, it is necessary to introduce the background knowledge of cosmology. Since general relativity's view of spacetime and dynamical equations are needed in order to understand modern cosmology, we briefly introduce these topics in the appendix. For the background cosmology, we first introduce the Robertson-Walker metric, the most general metric that is adapted to the cosmological principle, and derive dynamical equations from Einstein's equations with this metric. We then explore evolutions of a perfect fluid with given equations of state. Thereafter, we introduce the basic knowledge of particle physics, including standard model and beyond, as particle physics is essential to understand modern cosmology. After that, we explore the thermal history of the universe, i.e., the standard hot big bang model, reviewing important events in radiation , matter and dark energy dominated epochs respectively. On account of its similarity to dark energy, we introduce the primordial inflation model in the end of this part, a key modification to the hot big bang model.
We then survey dark energy models. Firstly, we explore the cosmological constant model and indicate two major problems within it, that is, the fine-tuning and coincidence problems. Because of these two problems and consideration from particle physics theories as well as the status quo of observational data, we introduce dynamical dark energy (DDE) models and survey the basic ideas of several important DDE models, including quintessence, phantom, quintom, k-essence and holographical dark energy.
Thereafter, we stick to the quintessence DDE models. By the definitions of the fine-tuning and coincidence problems in this thesis, DDE itself avoids the fine-tuning problem, so this part mainly focuses on how the quintessence models can alleviate the coincidence problem. We first briefly introduce the knowledge of autonomous dynamical system that is needed for analyzing the dynamics of quintessence. After simplifying the quintessence dynamical system, we focus on two types of models: tracking solutions and scaling solutions. Then we investigate implication of models that couple quintessence to ordinary matter for the coincidence problem.
Finally, we turn to the innovative part of this thesis. In this part, we take a new approach to reconstruct quintessence potentials. With this approach, we first easily obtain a tracking solution that is different from those discovered previously, and straightforwardly find a solution of multiple attractors, i.e., a solution with more than one attractor for a given set of parameters. Then we propose a scenario of quintessence where the field jumps out of the scaling attractor to the de-Sitter-like attractor, by introducing a field whose value changes a certain amount in a short time, leading to the current acceleration. We also calculate the change the field needs for a successful jump and suggest a possible mechanism that involves spontaneous symmetry breaking to realize the sudden change of the field value.
在进入动力学暗能量模型这个主题之前,本文先介绍必要的宇宙学背景知识.广义相对论的时空观和动力学方程对理解现代宇宙学是不可或缺的,我们把这方而的简单介绍列于附录中.关于背景宇宙学,我们先引入满足宇宙学原理的最一般的度规,即Robertson-Walker度规,再根据爱因斯坦方程推出在这个度规下的动力学方程,然后考察给定状态方程的理想流体的动力学演化.接着,我们介绍粒子物理的基本知识,包括标准模型和超出标准模型,因为现代宇宙学也离不开粒子物理.之后,我们考察宇宙的热历史,即标准热大爆炸模型,分别列举了在辐射,物质以及暗能量为主时期发生的各个重要事件.鉴于与暗能量的相似性,这部分最后介绍对热大爆炸模型的一个重要修正,即原初暴涨模型.
我们接下来讨论暗能量的各种模型.这部分先介绍宇宙学常数模型,并指出它的两个问题,即精细调节问题和巧合性问题.基于这两个问题以及粒子物理理论方面的考虑和观测数据的现状,我们引入动力学暗能量模型,并考察了几种主要的动力学暗能量模型的基本思想,包括Quintessence,Phantom,Quintom,K-essence和全息暗能量.
之后,我们把注意力集中于Quintessence动力学暗能量模型.根据本论文对精细调节问题和巧合性问题的定义,引入动力学暗能量本身已经避免了精细调节问题,所以这部分主要探讨Quintessence的动力学演化怎样缓解巧合性问题.我们先简单介绍分析Quintessence的演化所需的自治动力学系统的知识.在化简Quintessence动力学系统之后,我们着重讨论两类模型:Tracking解和Scaling解.然后,我们考察与物质耦合的Quintessence模型对巧合性问题的启示.
最后我们进入本论文的创新性工作部分.这部分我们先引入一种新的重建Quintessence势的方法.用这种方法,我们很容易地得到一个以前没有发现的Tracker解,并很直接地得到一个多重吸引子解,即,在给定参数下有多于一个吸引子的解.然后,我们提出一个新的Quintessence模型.在这个模型中,Quintessence场,通过其场值在很短时间内的变化,从一个Scaling吸引子跳到一个类de Sitter吸引子使宇宙加速膨胀.我们接着计算了这样的跳跃所需的场值变化,并提出一个基于自发对称破缺的机制,来实现这个场值的突变.
The proposing of inflation theory in the early 1980s suggested the birth of particle cosmology, while the discovery of dark energy in 1998 has made it one of the hottest research areas in physics. On the other hand, various experiments in cosmology since the early 1990s, including COBE and WMAP, have measured cosmological parameters to high precision and been found to be in good agreement with cosmological theories like inflation, pronouncing the coming of the era of precision cosmology.
Before going into dynamical dark energy models, it is necessary to introduce the background knowledge of cosmology. Since general relativity's view of spacetime and dynamical equations are needed in order to understand modern cosmology, we briefly introduce these topics in the appendix. For the background cosmology, we first introduce the Robertson-Walker metric, the most general metric that is adapted to the cosmological principle, and derive dynamical equations from Einstein's equations with this metric. We then explore evolutions of a perfect fluid with given equations of state. Thereafter, we introduce the basic knowledge of particle physics, including standard model and beyond, as particle physics is essential to understand modern cosmology. After that, we explore the thermal history of the universe, i.e., the standard hot big bang model, reviewing important events in radiation , matter and dark energy dominated epochs respectively. On account of its similarity to dark energy, we introduce the primordial inflation model in the end of this part, a key modification to the hot big bang model.
We then survey dark energy models. Firstly, we explore the cosmological constant model and indicate two major problems within it, that is, the fine-tuning and coincidence problems. Because of these two problems and consideration from particle physics theories as well as the status quo of observational data, we introduce dynamical dark energy (DDE) models and survey the basic ideas of several important DDE models, including quintessence, phantom, quintom, k-essence and holographical dark energy.
Thereafter, we stick to the quintessence DDE models. By the definitions of the fine-tuning and coincidence problems in this thesis, DDE itself avoids the fine-tuning problem, so this part mainly focuses on how the quintessence models can alleviate the coincidence problem. We first briefly introduce the knowledge of autonomous dynamical system that is needed for analyzing the dynamics of quintessence. After simplifying the quintessence dynamical system, we focus on two types of models: tracking solutions and scaling solutions. Then we investigate implication of models that couple quintessence to ordinary matter for the coincidence problem.
Finally, we turn to the innovative part of this thesis. In this part, we take a new approach to reconstruct quintessence potentials. With this approach, we first easily obtain a tracking solution that is different from those discovered previously, and straightforwardly find a solution of multiple attractors, i.e., a solution with more than one attractor for a given set of parameters. Then we propose a scenario of quintessence where the field jumps out of the scaling attractor to the de-Sitter-like attractor, by introducing a field whose value changes a certain amount in a short time, leading to the current acceleration. We also calculate the change the field needs for a successful jump and suggest a possible mechanism that involves spontaneous symmetry breaking to realize the sudden change of the field value.
引文
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