引力与空间层展

发布时间：2018-08-13 16:23

【摘要】：黑洞热力学的发现揭示了引力系统与热力学系统存在深刻的联系,物理学家开始猜测,引力可能是一种层展现象而非基本作用力。1995年Jacobson通过局域Rindler视界上的克劳修斯关系导出了爱因斯坦场方程更是增强了这个信心。另一方面,通过对黑洞熵的研究,Susskind和t Hoof提出了全息原理,它认为一个d+1维的引力系统自由度与其d维边界上非引力系统自由度存在对应。全息原理被认为可能是量子引力的一个基本原理,同时它实际上也是层展观点的依据之一。最近,Padmanabhan将引力的层展观点应用到宇宙学,并提出全息均分原理,它认为宇宙的膨胀源于层展空间的表面自由度与体自由度之差,将全息均分应用到FRW宇宙的Hubble视界上可以得到标准的Friedmann方程。通过对Padmanabhan提出的空间层展方程的不同修正,这也可以推广到高维爱因斯坦引力、Gauss-Bonnet引力和更普遍的Lovelock引力。另外,这种不同的修正也可以通过将Padmanabhan的方程中表面自由度与体自由度之差代之为它的函数,这被称为更普遍的全息均分律。然而这些推广只能得到空间平直下FRW宇宙的Friedmann方程,为了能导出任意空间曲率Friedmann方程,还需要修改方程并将之应用到表观视界上。通过具体分析这种新的空间层展观点以及上述各类推广,我们发现实际上这些不同的修正可以用一个统一的方程描述,而它们实际上是该方程的特例。进一步我们将该方程应用到f(R)引力和变形Horava-Lifshitz引力下FRW宇宙,并得出层展观点下修正的动力学演化方程。在相应的极限条件下,n=3,f(R)=R,以及ω→0,这些动力学方程能退回到广义相对论下的情形,表现出很好的一致性。另一方面,由于在高维爱因斯坦引力、Gauss-Bonnet引力和Lovelock引力下所作推广中,应用在Hubble视界上的全息均分原理得不出任意空间曲率的Friedmann方程,我们重新推导了在表观视界下全息均分原理的表达形式,并成功得到任意空间曲率的Friedmann方程。我们认为,这种差别可能是因为在这些推广的引力理论下全息均分原理实际上适用于表观视界而不再适用于ubble视界。最后,女口Padmanabhan所言,新的层展观点给宇宙学提供了新的范式,我们考察了空间层展观点下de Sitter宇宙,在全息均分原理满足的情况下,得到状态参数ω和能量密度非常强的限制形式。由于在宇宙早期暴涨和动力学暗能量下的晚期宇宙都可能形成deSitter相,我们认为这将对暴涨模型和暗能量模型带来约束。
[Abstract]:The discovery of the thermodynamics of black holes reveals a deep connection between gravitational and thermodynamic systems, and physicists begin to speculate, Gravity may be a layer representation rather than a basic force. In 1995 Jacobson derived the Einstein field equation from the local Rindler horizon. On the other hand, by studying the entropy of black hole, Susskind and t Hoof put forward the holographic principle, which holds that the degree of freedom of a d-1-dimensional gravitational system corresponds to the degree of freedom of a non-gravitational system on its d-dimensional boundary. The holographic principle is considered to be a basic principle of quantum gravity, and it is actually one of the bases of the theory of layering. Padmanabhan has recently applied the idea of stratification of gravity to cosmology, and has proposed the principle of holographic equalization, which holds that the expansion of the universe is due to the difference between surface and volume degrees of freedom. The standard Friedmann equation can be obtained by applying the holographic equalization to the Hubble horizon of the FRW universe. By modifying the spatial layer expansion equation proposed by Padmanabhan, it can also be extended to the high-dimensional Einstein gravitational Gauss-Bonnet gravitation and the more general Lovelock gravitation. In addition, the difference between the surface and volume degrees of freedom in the Padmanabhan equation can be replaced by its function, which is called the more general holographic equalization law. However, these generalizations can only obtain the Friedmann equation of the FRW universe under space flatness. In order to derive the Friedmann equation of arbitrary space curvature, it is necessary to modify the equation and apply it to the apparent horizon. Through the analysis of this new view of spatial layering and the generalization mentioned above, we find that in fact these different modifications can be described by a unified equation, and they are in fact special cases of the equation. Furthermore, we apply the equation to the FRW universe under f (R) gravity and deformed Horava-Lifshitz gravity, and obtain the modified dynamic evolution equation from the viewpoint of stratification. Under the corresponding limit conditions, the dynamic equations can be retreated to the general relativistic case and show good consistency. On the other hand, because of the generalization of the high dimensional Einstein gravity Gauss-Bonnet gravity and Lovelock gravity, the holographic equalization principle applied to the Hubble horizon can not obtain the Friedmann equation of arbitrary space curvature. We rederive the expression of the holographic equalization principle under the apparent horizon and successfully obtain the Friedmann equation of arbitrary space curvature. We believe that this difference may be due to the fact that the holographic equalization principle is actually applicable to the apparent horizon but no longer to the ubble horizon under these generalized gravitational theories. Finally, according to Padmanabhan, the new view of layering provides a new paradigm for cosmology. We examine the de Sitter universe in the view of spatial layering, where the holographic equalization principle is satisfied. The limiting form of state parameter 蠅 and energy density is obtained. Since the deSitter phase may be formed in the late universe under both the early cosmic explosion and the dynamic dark energy, we believe that this will bring constraints to both the skyrocketing model and the dark energy model.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P145.8;P131

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