与引力非最小耦合的标量场暗能量模型

发布时间：2018-05-17 17:39

本文选题：宇宙加速膨胀 + 暗能量　；参考：《湖南师范大学》2016年博士论文

【摘要】：1998年,天文学家尝试利用Ia型超新星的观测数据来探测宇宙膨胀减慢的速率,却意外地发现我们的宇宙正在做加速膨胀,相继有大量的观测数据验证了这一结果。人们从两个方面来解释宇宙当今的加速膨胀：修改爱因斯坦引力理论或者假设整个宇宙空间充斥着一种具有负压的特殊物质：暗能量。观测数据表明如果是暗能量主导着宇宙当今的演化,那它大约占所有宇宙能量的70%。暗能量最简单的候选者是宇宙学常数,它很好地与现有的观测结果相吻合,但是存在两个至今未能解决的理论问题,即微调问题和巧合问题。此外,物理学家从暴胀宇宙学中得到启示,引入了一些标量场来作为暗能量的候选者,如Quintessence、Phantom和Quintom等。与引力非最小耦合的标量场暗能量模型(以下简称非最小耦合模型)不同于普通的标量场暗能量模型是因为在其拉氏量中存在标量场与引力场的相互耦合。该模型不仅可以解释宇宙早期的暴胀,还可以很好地解释宇宙当今的加速膨胀。本文我们主要研究非最小耦合模型,对曲率标量考虑了两种不同的形式：度规形式和Palatini形式。我们首先介绍了非最小耦合模型的动力学行为和有效状态方程参数的演化,发现在Palatini形式下其有效状态方程参数不仅可以穿越-1分界线,而且在-1附近出现了振荡行为,这是有别于度规形式的一个新特性。同时,在Palatini形式中宇宙将最终进入由暗能量主导的de-Sitter相。接着讨论了非最小耦合模型的线性微扰理论。我们利用度规形式和Palatini形式的背景场方程和微扰方程,分析了引力势、有效牛顿引力常数和物质微扰的线性增长过程,并将结果和最小耦合模型以及宇宙学常数(A Cold Dark Matter,简称ACDM)模型进行了比较。我们发现度规形式和Palatini形式下非最小耦合模型的区别主要集中在低红移区域,但目前的观测数据还不能够有效地区分这两种不同形式的非最小耦合模型。然后研究了度规形式和Palatini形式下非最小耦合模型的integra-ted Sachs-Wolfe(ISW)效应和功率谱。发现其ISW效应依赖于哈勃因子H(a)、物质微扰的线性增长函数D+(a)、无量纲物质密度因子Ωm(a)和耦合函数F(a)。当耦合常数为负时,度规形式和Palatini形式之间以及它们与ACDM模型之间的区别可以忽略不计,因此均可使用ACDM模型来代替进行研究。而耦合常数为正时,Palatini形式的非最小耦合模型与ACDM模型的偏离程度最大,并且度规形式和Palatini形式之间的区别也非常明显。最后我们把非最小耦合模型的线性微扰理论推广到非线性区域,研究了度规形式和Palatini形式下非最小耦合模型的球塌缩过程。我们发现所有的非最小耦合模型在高红移区域的行为都趋于Einstein de Sitter(EdS)模型,并且当耦合常数为负时,非最小耦合模型与ACDM模型的差别几乎可以忽略。
[Abstract]:In 1998, astronomers tried to use the observational data of the Ia supernova to detect the rate of cosmic expansion slowing down, but unexpectedly we found that our universe is accelerating expansion, and there is a large amount of observation data to verify this result. People explain the accelerating expansion of the universe in two ways: modifying the Einstein theory of gravity or It is assumed that the whole cosmic space is full of a special material with negative pressure: dark energy. Observation data show that if dark energy is leading the evolution of the universe today, the simplest candidate for the 70%. dark energy of all cosmic energy is the cosmological constant, which is well consistent with the existing observations, but there is two In addition, the physicists have gained inspiration from the expansion of cosmology and introduced some scalar fields as candidates for dark energy, such as Quintessence, Phantom and Quintom, and the dark energy model of the scalar field with non minimum coupling of gravitation (hereinafter referred to as the non minimum coupling model). Different from the ordinary scalar field, the dark energy model is due to the mutual coupling between the scalar field and the gravitational field in its Lagrangian. This model can not only explain the early expansion of the universe, but also explain the accelerated expansion of the universe. In this paper, we mainly study the non minimum coupling model and consider two different kinds of curvature scalars. Form: the formal form and the Palatini form. We first introduce the evolution of the dynamic behavior and the effective state equation parameters of the non minimum coupling model. It is found that the effective state equation parameters in the Palatini form can not only pass through the -1 boundary, but also oscillate near the -1, which is different from the formal form. Meanwhile, in the form of Palatini, the universe will eventually enter the de-Sitter phase dominated by dark energy. Then the linear perturbation theory of the non minimum coupling model is discussed. We use the background equation and perturbation equation of the metric form and Palatini form to analyze the gravitational potential, the effective Newton gravitational constant and the linear growth of the matter perturbation. The results are compared with the minimum coupling model and the A Cold Dark Matter (ACDM) model. We find that the difference between the metric form and the non minimum coupling model under the Palatini form is mainly concentrated in the low red shift region, but the current observation data can not be effectively divided into the two different forms of the non minimum. The small coupling model. Then we study the integra-ted Sachs-Wolfe (ISW) effect and power spectrum of the non minimum coupling model in the formal form and the Palatini form. It is found that the ISW effect depends on the Harbert factor H (a), the linear growth function of the matter perturbation D+ (a), the dimensionless substance density factor Omega m (a) and the coupling function F. The difference between the regular form and the Palatini form and the difference between them and the ACDM model can be ignored, so the ACDM model can be used instead of the study. While the coupling constant is positive, the non minimum coupling model of the Palatini form is most deviated from the ACDM model, and the difference between the metric form and the Palatini form is also very different. In the end, we generalize the linear perturbation theory of the non minimum coupling model to the nonlinear region, and study the spherical collapse process of the non minimum coupling model in the form of the metric and the Palatini form. We find that all the behavior of the non minimum coupling model in the high redshift region tends to Einstein de Sitter (EdS) model and is a coupling constant. The difference between the non minimum coupling model and the ACDM model is negligible.
【学位授予单位】：湖南师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P159

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