关于当前宇宙加速膨胀若干问题的物理研究

发布时间：2018-09-08 12:36

【摘要】： 目前,通过对Ia型超新星观测以及对源于Wilkinson Microwave AnisotropyProbe(WMAP)精确数据的分析表明我们的宇宙目前正处于加速膨胀的阶段。这与以普通重子物质为基础的热大爆炸宇宙学模型相矛盾。按照热大爆炸宇宙学模型的观点,宇宙应该是减速膨胀的。为了能够在热大爆炸宇宙学模型的框架下解释宇宙当前的加速膨胀,就要对其进行修正。修正的方式主要有两种,一是通过在宇宙组分中引入一种新的、具有负压强的、且在大尺度结构中是均匀分布的动力学成分,即所谓的暗能量。这实际上是对Einstein引力场方程的右边进行了修正。这种修正的正确性是由Wilkinson Microwave AnisotropyProbe(WMAP)所支持。该探测显示,暗能量占宇宙物质总成分的73%。因此,有理由认为它是当前宇宙加速膨胀的诱因。二是通过对Einstein引力场方程的左边,即时空几何部分,进行修正。这类修正通常被称为引力修正理论,f(R)引力理论就是其中较具竞争力的一个。本文分别从上述两个途径入手,对当前加速膨胀宇宙中的若干物理问题进行了研究。首先,对作为暗能量与暗物质统一模型的新的广义Chaplygin气体进行了讨论。我们不仅分别讨论了当暗能量和暗物质之间存在和不存在相互作用时,能量密度随红移z的演化趋势,而且还给出了暗能量和暗物质间能量转移的演化规律。同时,标记转移强度常数的今天值也被给出。为了考察该模型对结构形成的影响,我们给出了其增长因子的演化轨迹。并将其与广义Chaplygin气体和ΛCDM模型增长因子的演化轨迹进行了比较。最后运用Om诊断对新的广义Chaplygin气体,广义Chaplygin气体和ΛCDM模型进行了区分。其次,我们在Raychaudhuri方程的基础上,导出了物质与几何间存在任意耦合时f(R)引力中的四种能量条件,即强能量条件,零能量条件,弱能量条件和主能量条件。同时,我们还导出了在物质与几何间存在任意耦合的f(R)引力中使引力保持吸引的条件和Dolgov-Kawasaki不稳定性判据。本文中得到的能量条件和Dolgov-Kawasaki不稳定性判据具有普适性,它囊括了f(R)引力中当物质与几何间存在非最小耦合时,无耦合时以及广义相对论的情况。为了看清四个能量条件和Dolgov-Kawasaki不稳定性判据在具体模型中的含义,我们考虑了一类f(R)模型。最后,我们讨论了如何在物质与几何间存在非最小耦合的f(R)引力中实现当前宇宙的加速膨胀。在幂律暴涨和态方程小于-1/3的条件下,我们给出了模型中参数间的关系以及在该模型中当前宇宙加速膨胀的条件和物质候选者。
[Abstract]:At present, the observation of Ia supernova and the analysis of precise data from Wilkinson Microwave AnisotropyProbe (WMAP) show that our universe is in the stage of accelerating expansion. This contradicts the thermal Big Bang cosmological model based on ordinary baryon matter. According to the thermal Big Bang cosmological model, the universe should be decelerating and expanding. In order to explain the current accelerating expansion of the universe within the framework of the thermal Big Bang cosmological model, it is necessary to modify it. There are two main ways of correction, one is by introducing a new kind of dynamic component with negative pressure and uniform distribution in large scale structure, that is, the so-called dark energy. This is actually a correction to the right side of the Einstein gravitational field equation. The correctness of this correction is supported by Wilkinson Microwave AnisotropyProbe (WMAP). The probe shows that dark energy accounts for 73 percent of the total composition of cosmic matter. Therefore, there is reason to think that it is the cause of the current accelerating expansion of the universe. The second is to modify the left side of the Einstein gravitational field equation, that is, the geometry of space-time. This kind of correction is usually called the gravitational correction theory / (R) 's gravitation theory is one of the more competitive. In this paper, some physical problems in the accelerating expansion universe are studied from the above two approaches. Firstly, a new generalized Chaplygin gas is discussed as a unified model of dark energy and dark matter. We not only discuss the evolution trend of energy density with redshift z when there is and no interaction between dark energy and dark matter, but also give the evolution law of dark energy and energy transfer between dark matter and dark matter. At the same time, the today's value of the label transfer intensity constant is also given. In order to investigate the influence of the model on the formation of the structure, we give the evolution trajectory of the growth factor. The evolution trajectories of the growth factors in the generalized Chaplygin gas model and the CDM model are compared. Finally, the new generalized Chaplygin gas, the generalized Chaplygin gas and the CDM model are distinguished by using the Om diagnosis. Secondly, on the basis of Raychaudhuri equation, we derive four kinds of energy conditions in f (R) gravitation, that is, strong energy condition, zero energy condition, weak energy condition and principal energy condition, when there is any coupling between material and geometry. At the same time, we also derive the conditions for the attraction of f (R) gravity in the case of arbitrary coupling between matter and geometry and the criterion of Dolgov-Kawasaki instability. The energy condition and the Dolgov-Kawasaki instability criterion obtained in this paper are universal, which covers the case of f (R) gravitation when there is a non-minimum coupling between matter and geometry, and when there is no coupling, as well as the general relativistic theory. In order to understand the meaning of the four energy conditions and the Dolgov-Kawasaki instability criterion in the concrete model, we consider a class of f (R) model. Finally, we discuss how to accelerate the expansion of the current universe in f (R) gravity, where there is a non-minimum coupling between matter and geometry. Under the condition that the power law surge and the equation of state are less than -1 / 3, we give the relations between the parameters in the model, the conditions for accelerating the expansion of the universe and the material candidates in this model.
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2010
【分类号】：P159.3

【共引文献】