【作者】 黄河；

【导师】 余洪伟；

【作者基本信息】 湖南师范大学 ， 理论物理， 2015， 博士

【摘要】 广义相对论自提出以来,经受住了各种实验和观测的挑战,也对许多学科产生了深远的影响。标准的大爆炸宇宙学建立在广义相对论与宇宙学原理之上,被视为宇宙学中的标准模型,它可以成功地解释宇宙从大爆炸之后0.01秒到现在的整个演化历史。然而,它却面临着四个自己无法解决的理论问题：视界问题、平坦性问题、磁单极问题以及大爆炸奇点问题。1980年,美国物理学家Alan Guth首先提出了宇宙的暴胀理论,该理论认为宇宙在其极早期经历了一个短暂的、以指数形式膨胀的阶段。暴胀理论合理地解决了标准宇宙学模型中的视界问题、平坦性问题和磁单极问题,但对大爆炸奇点问题却无能为力。在标准宇宙学中,根据霍金等人提出的奇点定律,宇宙必定有一个开端,而这个开端便是所谓的大爆炸奇点。在奇点处,宇宙的能量密度和温度为无限大,现有物理理论全部失效。所以,如果某种理论能绕开奇点问题,毫无疑问是一种很有吸引力的方案。自生宇宙模型便是一种不包含奇点的宇宙学模型,该模型提出：宇宙最初起源于一个有限大小的爱因斯坦静态宇宙而非奇点,随后可进入暴胀时期。这样,自生宇宙模型就能顺利地与标准宇宙学模型融合起来。所以,爱因斯坦静态宇宙能否长时间地保持稳定状态对于自生宇宙模型是至关重要的。然而,值得注意的是：在广义相对论的框架下,考虑到各种涨落的扰动,爱因斯坦静态宇宙是不稳定的。因此,爱因斯坦静态宇宙在各种引力理论中的稳定性是一个值得人们深入研究的问题。除了自生宇宙模型,人们提出了很多有趣的方案用以解决奇点问题,例如弦理论／M理论中的循环宇宙模型和振荡宇宙模型。爱因斯坦静态宇宙的稳定性问题在很早就得到了人们的关注。早在1930年,爱丁顿首先发现在广义相对论的框架下由普通物质组成的爱因斯坦静态宇宙对于空间均匀且各项同性的扰动是不稳定的。此后,人们研究了在不同引力理论下,爱因斯坦静态宇宙对于不同类型扰动的稳定性问题。例如,圈量子引力(loop quantum gravity)、膜世界模型(braneworld model)、f(T)引力、f(R)引力、有质量引力(massive gravity)。Modified Gauss-Bonnet(mGB)引力是一种修改引力的理论,它的作用量是在广义相对论采用的爱因斯坦-希尔伯特作用量的基础上加上了个f(G)项,其中G是指Gauss-Bonnet不变量。在本文第三章中,在modified Gauss-Bonnet(mGB)引力中,我们假定宇宙的物质组分分别是由理想流体和标量场。对于理想流体的情况,结果可以发现：对于均匀的标量扰动,稳定的爱因斯坦静态解是存在的；而对于非均匀的标量扰动,由于当波数k趋近于无穷时,模型参数α不存在稳定性区间,所以并不存在稳定的爱因斯坦静态解。而对于标量场的情况,同理,我们发现：对于均匀和非均匀的标量扰动,均不存在稳定的爱因斯坦静态解。我们指出,个成功的自生宇宙模型要求：宇宙在过去无穷远的时候能够长期而稳定地处于爱因斯坦静态,此外,它还能很自然地从这个初态退出,然后进入暴胀阶段。我们的分析表明自生宇宙模型虽然可以避免大爆炸奇点,但是在·modified Gauss-Bonnet引力中无法实现,因为并不存在稳定的爱因斯坦静态解。Jordan-Brans-Dicke(JBD)引力理论是标量张量引力理论中的一种特殊情况。Jordan-Brans-Dicke引力理论能很自然地出现在超引力,Kaluza-Klein理论以及弦理论之中,而且它能用来解释从宇宙膨胀、宇宙极早期的暴胀以及宇宙晚期的加速膨胀。在本文第四章中,在Jordan-Brans-Dicke(JBD)引力框架下,我们假定宇宙的物质组分分别是由理想流体和标量场。对于理想流体的情况,我们的结果表明：爱因斯坦静态宇宙对于同时考虑均匀和非均匀扰动都是存在稳定解的。而对于标量场的情况,同理,可以发现：爱因斯坦静态宇宙对于同时考虑均匀和非均匀扰动也都是存在稳定解的。最后,我们指出：对于一个物质组分为标量场ψ的宇宙,它能够从稳定的爱因斯坦初态退出,然后自然地进入暴胀阶段。所以,在JBD引力中的自生宇宙模型是能够成功地解决奇点问题的。更多还原

【Abstract】 Since general relativity was formulated, it has withstood challenges from var-ious experiments and observations, influencing many disciplines profoundly. The standard big-bang cosmological model based on general relativity and the cosmo-logical principle can successfully explain the history of cosmic evolution from to the present one percent of a second after the big bang. However, the model confronts four theoretically unsolved problems:the horizon problem, the flatness problem, the magnetic monopole problem and the big-bang singularity problem. In 1980, American physicist Alan Quth initially proposed the cosmic inflation which indi-cates the universe in the very early epoch underwent a transient and exponentially rapid expansion. Cosmic inflation reasonably explains the horizon problem, the flatness problem, the magnetic monopole problem, leaving the big-bang singularity unsolved. According to the singularity theorem presented by Hawking and others, the universe must have a beginning which is the so-called big-bang singularity. At the singularity, all the physical theories are invalid because infinitely large are both the temperature and energy density of the universe. Thus, some theories should be attractive if they can circumvent the singularity. The emergent universe is a cosmological model without the singularity. It assumes that the universe originats from an Einstein static universe with finite scale rather than a singularity, and then enters the inflationary stage. So, the emergent theory can be accommodated with the standard cosmological model. Thus, it is quite crucial for emergent theo-ry whether Einstein static universes can keep stable past eternally. However, it is worth noting that an Einstein static universe is unstable within general relativity, and it will lose stability against some perturbations. Therefore, it cannot stay at the initial static state past eternally. Thus, it is worth to discuss the stability of Einstein static universes. Besides the emergent universe scenario, some interesting models are proposed to solve the singularity problem, such as cyclic scenarios in string/M theory and the oscillating universes.The stability of Einstein static universes attracted much attention a long time ago. In 1930, Eddington initially found that an Einstein static universe with the content of normal matter is unstable with respect to spatially homogeneous and isotropic scalar perturbations in the framework of general relativity. Since then, the stability of Einstein static universe in various theories of gravity—such as in loop quantum cosmology, braneworld scenario, f(T) gravity, f(R) gravity and massive gravity, has been investigated against different kinds of perturbations.Modified Gauss-Bonnet gravity is a modified theory of gravity which adds a f(G) term on the original Einstein-Hilbert action, where G is the Gauss-Bonnet invariant. In Chapter III, we investigate the stability of Einstein static universes within the framework of modified Gauss-Bonnet gravity. We assume that the matter component consists of a perfect fluid with a constant equation of state and a scalar field, respectively. For the scenario of perfect fluid, it is concluded that there are stable Einstein static solutions against homogeneous scalar perturbations and there exists no stable ES solution against homogeneous scalar perturbations since model parameter a has no stability region as wavenumber k approximates infinity. In the same way, For the case of a scalar field; it is shown that there are no stable Einstein static solutions against both homogeneous and inhomogeneous scalar perturbations. Finally, we must point out that since a successfully emergent scenario requires that the universe stays at a stable ES state past eternally, and furthermore, that it can naturally exit from this state and then enter an inflationary era, our analysis suggests that the emergent scenario that avoids the big bang singularity cannot be realized in the modified GB gravity since there are no stable ES solutions in the first place.The Jordan-Brans-Dicke (JBD) theory of gravity is a particular example of the scalar-tensor theories of gravity. The JBD theory of gravity may appear naturally in supergravity, Kaluza-Klein theory, and string theory and it has been employed to elucidate the cosmic expansion ranging from the early cosmic inflation to the late time cosmic acceleration. In Chapter IV, We assume that the matter con-tent consists of a perfect fluid with a constant equation of state and a scalar field, respectively. For the case of perfect fluid, we find that within the framework of the Jordan-Brans-Dicke (JBD) theory of gravity there exist stable Einstein static solutions against both homogeneous and inhomogeneous scalar perturbations. In the same way, if the matter content of the universe consists in a scalar field Ψ, there exist stable Einstein static solutions against homogeneous and inhomoge-neous scalar perturbations. Finally, we point out that the universe can exit from this stable state and then enter an inflationary phase naturally. As a result,the emergent scenario in the JBD theory may resolve the big bang singularity problem successfully.更多还原