本文選題：修改引力 + 暗能量��； 參考：《中國科學(xué)技術(shù)大學(xué)》2011年碩士論文

【摘要】：最近十年,宇宙的加速膨脹一直是物理學(xué)一個(gè)非常重要的問題。宇宙學(xué)家們嘗試了很多模型試圖來作出解釋,比較認(rèn)可的是宇宙學(xué)常數(shù),或者暗能量的模型。另外,通過修改引力的模型也是一個(gè)非常有競爭力的模型。比如有通過引力一個(gè)標(biāo)量場與引力場的非最小耦合,還有通過將Einstein-Hilbert作用量擴(kuò)展為里奇標(biāo)量R的函數(shù)也就是f(R)理論。這些理論都是建立在愛因斯坦的將引力解釋成撓率為零而曲率不為零的流形上面。另一方面,從最早愛因斯坦開始,就還有一種對(duì)引力的解釋,那就是將引力解釋成曲率為零而撓率不為零的背景流形。這樣,我們可以定義一個(gè)撓率標(biāo)量T作為最簡單的拉氏量,類似于廣義相對(duì)論里的里奇標(biāo)量R。同樣,我們?cè)噲D將拉氏量推廣成T的函數(shù)也就是本文所要討論的f(T)理論。f(T)引力的運(yùn)動(dòng)方程可以寫成等效的弗里得曼方程的形式,其中有一部分可以解釋成等效的暗能量,從而可以作為一個(gè)解釋宇宙加速膨脹的模型。它的一個(gè)最顯著的優(yōu)勢在于,不像f(R)里的運(yùn)動(dòng)方程是四階的方程, f(T)的運(yùn)動(dòng)方程只是二階的。 考慮到這個(gè)理論里沒有Lorentz對(duì)稱性,因而相比于廣義相對(duì)論(GR),這個(gè)理論會(huì)多出一些自由度,而且,這些多出的自由度不會(huì)在度規(guī)里體現(xiàn)出來,只能在標(biāo)架里來定義。之前的文獻(xiàn)都忽略了這一點(diǎn)。本文在標(biāo)架里定義了所有可能出現(xiàn)的標(biāo)量自由度。通過對(duì)作用量變分,得到這個(gè)理論的運(yùn)動(dòng)方程的表達(dá)式。然后寫成零階和一階的形式分別得到背景和擾動(dòng)的演化方程。這里擾動(dòng)的運(yùn)動(dòng)方程是最一般的,但我們的分析僅限于物質(zhì)主導(dǎo)時(shí)期宇宙大尺度結(jié)構(gòu)演化,因而可以設(shè)定壓強(qiáng)及其擾動(dòng)為零。通過分析擾動(dòng)的運(yùn)動(dòng)方程,可以得到相對(duì)物質(zhì)密度擾動(dòng)的演化方程,它與GR里的方程有相同的形式,其差別僅在于不同的等效引力常數(shù)。選定初始條件,就可以數(shù)值求解這個(gè)微分方程,并對(duì)不同的理論進(jìn)行比較。
[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.
【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2011
【分類號(hào)】：P159.2

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