高斯—伯纳特项可以使宇宙加速膨胀吗？

发布时间：2018-04-30 23:18

本文选题：宇宙学 + 超新星宇宙学　；参考：《上海师范大学》2014年硕士论文

【摘要】：众所周知,我们的宇宙自大爆炸开始就一直在膨胀。但是对于宇宙到底是在加速膨胀还是在减速膨胀的讨论,直到1998年才得到答案。由佩尔马特(S.Perlmutter)领导的超新星宇宙学工程和施密特(B.Schmidt)所领导的高红移超新星研究小组,观测距离我们很远的宇宙中爆发的超新星,对我们所处的宇宙进行描绘。通过计算超新星与我们的距离以及它们远离我们的速度或者红移,得出了宇宙正在加速膨胀的结论。并且WMAP的数据与星系的大尺度分布更加确定了这一结论。因此,物理学家们提出了许多的宇宙学模型来解释宇宙的加速膨胀。首先,本文回顾了宇宙学的现状,宇宙学原理与标准宇宙学模型,并强调了宇宙学中除了状态函数之外的另一个重要参量——减速因子q,并对其取值与宇宙的膨胀进行了讨论。紧接着讨论了描述宇宙加速膨胀的几个模型,如：暴胀模型,宇宙学常数模型以及描述高维宇宙学的卡鲁扎-克莱茵理论,并对这几种模型的特点与理论上的不足做了大致回顾。其中重点介绍了卡鲁扎-克莱茵理论框架下的M理论,介绍了弦理论、超弦理论以及M理论的知识,重点讨论了M理论的膜世界模型。这个理论将真实宇宙看作是一个1+3维的膜(brane)嵌入了一个1+3+d维的bulk。标准模型粒子被束缚在了膜上,而引力却可以在bulk中自由传播。这一模型在低能情况下可以恢复到广义相对论,但是在高能量时引力“泄漏”到bulk中,表现出一种真正的高维的方式。接着举了膜世界模型中比较典型的RS-1与RS-2模型为例,介绍了他们的一些动力学性质。最后,回到膜世界宇宙学,并在膜世界模型的作用量中引入了高斯-伯纳特(Gauss-Bonnet)项。因为它的运动方程中不含有度规的两阶以上的导数项,高斯-伯纳特项在四维或者低于四维时表现为一个表面项,但在高维中具有动力学意义,在理论上它可以被解释为宇宙加速膨胀的原因。所以,我们利用超新星宇宙学,将Ia型超新星数据引入,去拟合模型中的耦合系数,并通过描绘状态函数、哈勃参数尤其是减速因子的函数图像,来检验高斯-伯纳特项是否可以成为宇宙加速膨胀的有力候选者。
[Abstract]:As we all know, our Big Bang has been expanding ever since. But the question of whether the universe is expanding or slowing was not answered until 1998. The Gao Hong supernova research group, led by Perlmut S. Perlmutter and Schmitt B. Schmidt, looks at supernovae in a distant universe and depicts the universe in which we live. By calculating the distance between supernovae and our speed or redshift away from us, we conclude that the universe is expanding faster. And the WMAP data and the large-scale distribution of galaxies confirm this conclusion. Therefore, physicists have proposed many cosmological models to explain the accelerating expansion of the universe. Firstly, this paper reviews the present situation of cosmology, cosmology principle and standard cosmology model, and emphasizes another important parameter in cosmology besides state function, deceleration factor Q, and discusses its value and expansion of the universe. Then several models describing the accelerating expansion of the universe are discussed, such as the inflation model, the cosmological constant model and the Kaluza-Klein theory of high-dimensional cosmology. The characteristics and theoretical deficiencies of these models are reviewed. The M theory under the framework of Kaluza-Klein theory, string theory, superstring theory and the knowledge of M theory are introduced, and the membrane world model of M theory is discussed emphatically. This theory regards the real universe as a 13 dimensional membrane brane) and embeds a 13 d dimensional bulk. Standard model particles are bound to the film, while gravity propagates freely in the bulk. This model can be restored to general relativity at low energy, but the gravitational "leakage" to bulk at high energy shows a true high-dimensional approach. Then the typical RS-1 and RS-2 models in the membrane world model are taken as examples and some of their dynamic properties are introduced. Finally, we return to the film world cosmology, and introduce the Gauss-Bonnet term in the action quantity of the membrane world model. Because its equation of motion does not contain more than two derivative terms of the metric, the Gauss-Bernaut term appears as a surface term in or below four dimensions, but has dynamic significance in high dimensions. In theory, it can be explained as the accelerating expansion of the universe. So we use supernova cosmology to introduce the Ia supernova data to fit the coupling coefficients in the model, and by describing the state function, the Hubble parameters, especially the function image of the deceleration factor, To test whether the Gauss-Bernat term can be a powerful candidate for accelerating expansion of the universe.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P159

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