暗能量與f（T）引力相關問題研究
發(fā)布時間：2018-12-06 11:51
【摘要】：本文對暗能量的巧合問題以及與暗能量相關的修改引力理論,f(T)引力,進行了研究。 首先是對三重巧合問題的研究。我們指出了目前比較流行的兩種三重相互作用暗能量模型之間的等價性。根據(jù)穩(wěn)態(tài)假設,我們求出了各能量分量之間的轉化項的具體形式,并發(fā)現(xiàn),符合穩(wěn)態(tài)假設的能在數(shù)學層面解決三重巧合問題的解有三組,但只有一組解是符合實際觀測的,這組解表明。在宇宙膨脹過程中,暗能量轉化為物質,物質又轉化成輻射,即：隨著宇宙膨脹,密度減小慢的能量密度向著密度減小快的能量密度轉化,以此來解決巧合問題。我們還對三重相互作用暗能量模型的穩(wěn)定性進行了全面研究,分析了所有的不同形式的相互轉化項及其組合,發(fā)現(xiàn)只有當物質和暗能量之間的轉化項正比于臨界密度,或者暗能量密度、且物質和輻射之間的轉化項不是正比于輻射密度時,對應的模型在微擾下才是穩(wěn)定的,這個結果對相關的模型構建給出了限制。 其次是在全息能量模型的基礎上,對f(T)引力理論重新構建的研究。由于f(T)是修改引力理論,它所修改的是引力理論中的幾何部分的內(nèi)容,而全息能量模型中的能量又是通過時空流形的幾何量來定義的,這種與時空幾何的共同聯(lián)系使我們可以將兩者結合起來,以全息能量模型作為對f(T)引力理論的約束,從而確定f(T)引力理論的作用量形式,使得最終得到的f(T)理論自動包含一個加速膨脹的宇宙學解。不同的全息能量模型會導致不同的f(T)引力理論。在本文中,我們對目前影響比較大的三種全息暗能量模型,HDE、NADE和RDE,分別進行了相應的f(T)引力理論的重新構建；我們也在我們自己建立的全息ρKMR模型的基礎上,進行了相應的f(T)引力理論的重新構建。在構建過程中,我們發(fā)現(xiàn),目前普遍采用的邊界條件可以在微分方程的通解中選出符合厄米性要求的解,在這個意義上來說,這些邊界條件是有一定合理性的,但是,它們會導致一些重要信息的丟失,比如在RDE的物質占主導時期,采用這些邊界調(diào)節(jié)得到的結果沒有展現(xiàn)出預期應該有rescaling行為,這是由于邊界條件過于粗糙造成的。我們提出了新的邊界調(diào)節(jié),并利用它們給出更加合理的結果。
[Abstract]:In this paper, the coincidence problem of dark energy and the modified gravitational theory, f (T) gravitation related to dark energy are studied. The first is the study of triple coincidences. We point out the equivalence between two kinds of triple interaction dark energy models which are popular at present. According to the steady-state hypothesis, we have worked out the specific form of the transformation terms between the energy components, and found that there are three groups of solutions which accord with the steady-state hypothesis to solve the triple coincidence problem at the mathematical level, but only one set of solutions is in accordance with the actual observation. This set of solutions shows that. In the process of cosmic expansion, dark energy is transformed into matter and matter is transformed into radiation. That is, with the expansion of the universe, the energy density decreases slowly and the energy density decreases quickly, thus solving the coincidental problem. We also study the stability of the triple interaction dark energy model and analyze all the different forms of transformation terms and their combinations. It is found that only when the transformation term between matter and dark energy is proportional to the critical density, Or the dark energy density, and the transformation term between matter and radiation is not directly proportional to the radiation density, the corresponding model is stable under perturbation, which limits the relevant model construction. Secondly, on the basis of holographic energy model, the reconstruction of f (T) gravity theory is studied. Since f (T) is a modified gravity theory, what it modifies is the geometric part of the gravity theory, and the energy in the holographic energy model is defined by the geometric quantities of the space-time manifold. This joint relationship with space-time geometry allows us to combine the two and take the holographic energy model as a constraint on f (T) 's gravitational theory, thus determining the form of the f (T) 's gravitational theory. The resulting f (T) theory automatically contains a cosmological solution that accelerates expansion. Different holographic energy models lead to different f (T) gravitational theory. In this paper, we reconstruct the three holographic dark energy models, HDE,NADE and RDE, respectively. On the basis of the holographic 蟻 KMR model, we have reconstructed the corresponding f (T) gravity theory. In the process of construction, we find that the commonly used boundary conditions can be selected from the general solutions of differential equations to meet Hermitian requirements. In this sense, these boundary conditions are reasonable, but, They can lead to the loss of important information, such as when RDE is dominated by substances, the results of these boundary adjustments do not show that there should be expected rescaling behavior, because the boundary conditions are too rough. We propose new boundary adjustments and use them to give more reasonable results.
【學位授予單位】：北京工業(yè)大學
【學位級別】：博士
【學位授予年份】：2013
【分類號】：P159
[Abstract]:In this paper, the coincidence problem of dark energy and the modified gravitational theory, f (T) gravitation related to dark energy are studied. The first is the study of triple coincidences. We point out the equivalence between two kinds of triple interaction dark energy models which are popular at present. According to the steady-state hypothesis, we have worked out the specific form of the transformation terms between the energy components, and found that there are three groups of solutions which accord with the steady-state hypothesis to solve the triple coincidence problem at the mathematical level, but only one set of solutions is in accordance with the actual observation. This set of solutions shows that. In the process of cosmic expansion, dark energy is transformed into matter and matter is transformed into radiation. That is, with the expansion of the universe, the energy density decreases slowly and the energy density decreases quickly, thus solving the coincidental problem. We also study the stability of the triple interaction dark energy model and analyze all the different forms of transformation terms and their combinations. It is found that only when the transformation term between matter and dark energy is proportional to the critical density, Or the dark energy density, and the transformation term between matter and radiation is not directly proportional to the radiation density, the corresponding model is stable under perturbation, which limits the relevant model construction. Secondly, on the basis of holographic energy model, the reconstruction of f (T) gravity theory is studied. Since f (T) is a modified gravity theory, what it modifies is the geometric part of the gravity theory, and the energy in the holographic energy model is defined by the geometric quantities of the space-time manifold. This joint relationship with space-time geometry allows us to combine the two and take the holographic energy model as a constraint on f (T) 's gravitational theory, thus determining the form of the f (T) 's gravitational theory. The resulting f (T) theory automatically contains a cosmological solution that accelerates expansion. Different holographic energy models lead to different f (T) gravitational theory. In this paper, we reconstruct the three holographic dark energy models, HDE,NADE and RDE, respectively. On the basis of the holographic 蟻 KMR model, we have reconstructed the corresponding f (T) gravity theory. In the process of construction, we find that the commonly used boundary conditions can be selected from the general solutions of differential equations to meet Hermitian requirements. In this sense, these boundary conditions are reasonable, but, They can lead to the loss of important information, such as when RDE is dominated by substances, the results of these boundary adjustments do not show that there should be expected rescaling behavior, because the boundary conditions are too rough. We propose new boundary adjustments and use them to give more reasonable results.
【學位授予單位】：北京工業(yè)大學
【學位級別】：博士
【學位授予年份】：2013
【分類號】：P159
【相似文獻】
相關期刊論文 前10條
1 許i，
本文編號：2365981
本文鏈接：http://sikaile.net/kejilunwen/tianwen/2365981.html
教材專著
