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arXiv 1610.09892gr-qc
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宇宙学和天体物理学应用中的引力扩展理论

Extended Theories of Gravity in cosmological and astrophysical applications

Aneta Wojnar

摘要:

博士论文的主要课题涉及Palatini f(R)引力和标量张量理论中考虑的宇宙学模型。我们介绍了一个简单的推广的LCDM模型的基础上Palatini修改的重力与二次Starobinsky项。由广义Chaobergin气体提供物质源。我们的模型的统计分析进行了调查。我们用动力系统的方法来研究宇宙的演化。该模型达到了一个非常好的协议与最新的实验数据,并产生一个暴胀时代所造成的第三类奇点。该模型还提供了当前的加速扩张。我们还表明,李和诺特对称性的方法是非常有用的工具,在宇宙学的考虑。我们研究了扩展引力理论(ETGs)的另外两个模型:新的混合度量-Palatini引力和最小耦合引力标量场。第一种方法适用于均匀和各向同性模型,而在标量张量理论中,我们研究各向异性宇宙。我们使用的对称性,以找到未知形式的潜在的,并解决经典的场方程在这两个模型。这些对称性对于寻找Wheeler-DeWitt方程的精确解和不变解也很有帮助。最后一部分我们在标量张量理论框架下研究相对论性恒星的平衡构型和稳定性条件。首先,我们证明了如果定义了广义能量密度和压力,则可以得到一类ETG的类TOV形式的平衡方程。根据我们的研究,中子星在最小耦合标量场模型下是一个稳定的系统。有一个补充,包括对称性以及动力系统方法的说明。并给出了应用实例。

英文摘要:

The main subjects of the PhD dissertation concern cosmological models considered in Palatini f(R) gravity and scalar-tensor theories. We introduce a simple generalization of the LCDM model based on Palatini modified gravity with quadratic Starobinsky term. A matter source is provided by generalized Chaplygin gas. The statistical analysis of our model is investigated. We use dynamical system approach to study the evolution of the Universe. The model reaches a very good agreement with the newest experimental data and yields an inflationary epoch caused by a singularity of the type III. The present-day accelerated expansion is also provided by the model. We also show that the Lie and Noether symmetry approaches are very useful tools in cosmological considerations. We examine two other models of Extended Theories of Gravity (ETGs): the novel hybrid metric-Palatini gravity and a minimally coupled to gravity scalar field. The first one is applied to homogeneous and isotropic model while in the scalar-tensor theory we study anisotropic universes. We use the symmetries in order to find unknown forms of potential and to solve classical field equations in both models. The symmetries also are very helpful in searching exact and invariant solutions of Wheeler-DeWitt equations. In the last part we are interested in equilibrium configurations and stability conditions of relativistic stars in the framework of scalar-tensor theories. Firstly, we show that TOV-like form of the equilibrium equations can be obtained for a wide class of ETGs if generalized energy density and pressure are defined. According to our studies, a neutron star is a stable system for the minimally coupled scalar field model. There is a supplement including notes on symmetries as well as dynamical systems approach. The illustrative examples of applications are also provided.

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