暗能量与f（T）引力相关问题研究
发布时间：2018-12-06 11:51
【摘要】：本文对暗能量的巧合问题以及与暗能量相关的修改引力理论,f(T)引力,进行了研究。 首先是对三重巧合问题的研究。我们指出了目前比较流行的两种三重相互作用暗能量模型之间的等价性。根据稳态假设,我们求出了各能量分量之间的转化项的具体形式,并发现,符合稳态假设的能在数学层面解决三重巧合问题的解有三组,但只有一组解是符合实际观测的,这组解表明。在宇宙膨胀过程中,暗能量转化为物质,物质又转化成辐射,即：随着宇宙膨胀,密度减小慢的能量密度向着密度减小快的能量密度转化,以此来解决巧合问题。我们还对三重相互作用暗能量模型的稳定性进行了全面研究,分析了所有的不同形式的相互转化项及其组合,发现只有当物质和暗能量之间的转化项正比于临界密度,或者暗能量密度、且物质和辐射之间的转化项不是正比于辐射密度时,对应的模型在微扰下才是稳定的,这个结果对相关的模型构建给出了限制。 其次是在全息能量模型的基础上,对f(T)引力理论重新构建的研究。由于f(T)是修改引力理论,它所修改的是引力理论中的几何部分的内容,而全息能量模型中的能量又是通过时空流形的几何量来定义的,这种与时空几何的共同联系使我们可以将两者结合起来,以全息能量模型作为对f(T)引力理论的约束,从而确定f(T)引力理论的作用量形式,使得最终得到的f(T)理论自动包含一个加速膨胀的宇宙学解。不同的全息能量模型会导致不同的f(T)引力理论。在本文中,我们对目前影响比较大的三种全息暗能量模型,HDE、NADE和RDE,分别进行了相应的f(T)引力理论的重新构建；我们也在我们自己建立的全息ρKMR模型的基础上,进行了相应的f(T)引力理论的重新构建。在构建过程中,我们发现,目前普遍采用的边界条件可以在微分方程的通解中选出符合厄米性要求的解,在这个意义上来说,这些边界条件是有一定合理性的,但是,它们会导致一些重要信息的丢失,比如在RDE的物质占主导时期,采用这些边界调节得到的结果没有展现出预期应该有rescaling行为,这是由于边界条件过于粗糙造成的。我们提出了新的边界调节,并利用它们给出更加合理的结果。
[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.
【学位授予单位】：北京工业大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：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.
【学位授予单位】：北京工业大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：P159
【相似文献】
相关期刊论文 前10条
1 许i，
本文编号：2365981
本文链接：https://www.wllwen.com/kejilunwen/tianwen/2365981.html
