多标量场宇宙动力学

【作者】 赵一斌；

【导师】 李新洲；

【作者基本信息】 上海师范大学 ， 天体物理， 2006， 硕士

【摘要】 本文以广义相对论为基本框架，使用微分方程及其定性理论，研究了宇宙演化中的两个问题，包括暗能量和宇宙极早期的暴涨。 本文包括五章内容。第一章简单介绍了标准宇宙学、热大爆炸宇宙学及暴涨模型等宇宙学基础知识，为后续讨论做好理论上的准备。 第二章介绍了宇宙学观测及理论上的最新进展，着重讨论了暗能量的两个最受关注的候选者，宇宙学常数和动力学场(quintessence)，引出后续章节。 通过指数势的吸引子解可以建立quintessence模型，并且指数势可以从弦理论或者M理论中导出。在第三章中，考虑了在包含正压流体(barotropic fluid)的FRW宇宙中具有双重指数势的标量场动力学演化，研究发现其渐近行为并不总是对应于单重指数势情形。通过引进动力学吸引子，使得模型的后期行为对初始条件不敏感，从而在一定程度上避免了精调问题。利用相空间分析研究这类双重指数势模型，结合数值计算，能够揭示这类宇宙模型的大多数性质。 第四章中首先引进了O(N)quintessence，同时将第三章的讨论推广到O(N)quintessence模型。 第五章中研究了用复标量场来解释暴涨和宇宙当前加速膨胀的可能性。 复标量场的对称性破缺被用来解释宇宙的极早期暴涨(inflation)和现今的加速膨胀。选择可以重正化的势能项，并且考虑了辐射和物质，同样利用相空间分析和数值计算，分析复标量场的演化。研究发现，复标量场的模部分对应于inflaton场，而角向部分对应于quintessence场，从而构建了一个更加自然的quintessential inflation模型。更多还原

【Abstract】 In this master dissertation, under the fundamental frame of general relativity, we study the dark energy and inflation in the early Universe.The thesis is consisted of five chapters. In Chapter 1, in order to make a theoretical preparation for the following discussion, we briefly review the basic theory of cosmology which includes the standard cosmology, the hot big bang cosmology and the cosmological inflation.In chapter 2, we report the recent cosmological observational results and the development of theory. The two logical possibilities for dark energy are the cosmological constant and quintessence, which has caught much attention ever since its invention and been mainly discussed.The properties of the attractor solutions of exponential potentials can lead to models of quintessence. And exponential potentials can arise from M theory. In chapter 3, we study the cosmological dynamics of barotropic fluid and scalar field with a double exponential potential and point out that the late-time asymptotic-behavior does not always corresponding to the single-exponential case. The dynamical attractor of the cosmological system has been employed to make the late time behaviors of the model insensitive to the initial condition of the field and thus alleviates the fine tuning problem. Combining the information from the critical points analysis with numerical solutions, we can reveal most of their properties.In chapter 4, firstly, we introduce the O(N) quintessence and make a new generalization to the discussion in chapter 3 for this model.In chapter 5, we wish to point out the possibility of using a complex scalar field to account for the inflationary stage and the current acceleration.A renormalizable complex scalar field Φ described by a lagrangian with a U(1) symmetry spontaneously broken at a high energy scale and explicitly broken by instanton effects at a much lower energy can account for both the early inflationary phase and the recent accelerated expansion of the Universe. We study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show that this model is a good match for the current astronomical observation. Therefore, this model is more natural to explain the two stages of acceleration.更多还原