f（T）引力的宇宙学扰动

发布时间：2018-06-22 16:04

本文选题：修改引力 + 暗能量　；参考：《中国科学技术大学》2011年硕士论文

【摘要】：最近十年,宇宙的加速膨胀一直是物理学一个非常重要的问题。宇宙学家们尝试了很多模型试图来作出解释,比较认可的是宇宙学常数,或者暗能量的模型。另外,通过修改引力的模型也是一个非常有竞争力的模型。比如有通过引力一个标量场与引力场的非最小耦合,还有通过将Einstein-Hilbert作用量扩展为里奇标量R的函数也就是f(R)理论。这些理论都是建立在爱因斯坦的将引力解释成挠率为零而曲率不为零的流形上面。另一方面,从最早爱因斯坦开始,就还有一种对引力的解释,那就是将引力解释成曲率为零而挠率不为零的背景流形。这样,我们可以定义一个挠率标量T作为最简单的拉氏量,类似于广义相对论里的里奇标量R。同样,我们试图将拉氏量推广成T的函数也就是本文所要讨论的f(T)理论。f(T)引力的运动方程可以写成等效的弗里得曼方程的形式,其中有一部分可以解释成等效的暗能量,从而可以作为一个解释宇宙加速膨胀的模型。它的一个最显著的优势在于,不像f(R)里的运动方程是四阶的方程, f(T)的运动方程只是二阶的。考虑到这个理论里没有Lorentz对称性,因而相比于广义相对论(GR),这个理论会多出一些自由度,而且,这些多出的自由度不会在度规里体现出来,只能在标架里来定义。之前的文献都忽略了这一点。本文在标架里定义了所有可能出现的标量自由度。通过对作用量变分,得到这个理论的运动方程的表达式。然后写成零阶和一阶的形式分别得到背景和扰动的演化方程。这里扰动的运动方程是最一般的,但我们的分析仅限于物质主导时期宇宙大尺度结构演化,因而可以设定压强及其扰动为零。通过分析扰动的运动方程,可以得到相对物质密度扰动的演化方程,它与GR里的方程有相同的形式,其差别仅在于不同的等效引力常数。选定初始条件,就可以数值求解这个微分方程,并对不同的理论进行比较。
[Abstract]:The accelerating expansion of the universe has been a very important issue in physics for the last decade. Cosmologists have tried a number of models to try to explain, more commonly cosmological constants, or models of dark energy. In addition, the model by modifying gravity is also a very competitive model. For example, there is a nonminimum coupling between a scalar field and a gravitational field by gravity, and a function called f (R) by extending the Einstein-Hilbert action to the Richie scalar R. These theories are based on Einstein's interpretation of gravity as a manifold with zero torsion and no curvature. On the other hand, from the beginning of Einstein, there has been another explanation of gravity, that is, gravity is interpreted as a background manifold whose curvature is zero and torsion is not zero. In this way, we can define a torsion T as the simplest Lagrangian, similar to the Ricky scalar R in general relativity. Similarly, we try to generalize Laplace's quantity to the function of T, which is the equation of motion of f (T) theory. F (T) gravity can be written into the equivalent Friedman equation, some of which can be interpreted as equivalent dark energy. This could serve as a model to explain the accelerating expansion of the universe. One of its most significant advantages is that, unlike the equation of motion in f (R), which is a fourth-order equation of motion, the equation of motion is only second-order. Considering that there is no Lorentz symmetry in this theory, compared with general relativity (gr), the theory will have some degrees of freedom, and these extra degrees of freedom will not be reflected in the metric, but can only be defined in the frame. Previous literature has ignored this. In this paper, all possible scalar degrees of freedom are defined in the frame. The expression of the equation of motion of this theory is obtained by the variation of action. Then the evolution equations of background and disturbance are obtained in the form of zero order and one order respectively. The equation of motion of perturbation is the most general here, but our analysis is limited to the evolution of the large-scale structure of the universe in the period of matter dominated, so that the pressure and its perturbation can be set to zero. By analyzing the equation of motion of perturbation, the evolution equation of perturbation of relative mass density can be obtained. It has the same form as the equation in gr, and the difference is only in the different equivalent gravitational constants. The differential equation can be solved numerically by selecting the initial conditions, and the different theories are compared.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：P159.2

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