【作者】 孙昌波；

【导师】 李新洲；

【作者基本信息】 上海师范大学 ， 计算数学， 2009， 博士

【摘要】 宇宙加速膨胀的发现,对现代物理理论提出了新的挑战,也对科学计算赋予了新的任务。当前,人类已经进入了精确宇宙学时代,这是以下述事实为标志的:利用大量观测数据,通过数值方法计算出精确结果,比较各类理论的异同点,选取其中最佳者。本文利用数值计算和解析方法,探讨了宇宙加速膨胀的一些相关问题,研究了两种加速宇宙模型,它们分别是粘滞Cardassian宇宙和标量挠率宇宙。本文由五个部分组成。我们首先介绍了宇宙的一些基本事实以及基于广义相对论的宇宙学基础,还对加速宇宙模型做了简单分类。在第二章中,我们讨论了粘滞Cardassian宇宙模型的动力学和位力化。动力学分析结果表明:引入粘滞系数后,相空间存在一条临界线。与没有粘滞的情况相比,PL模型态方程参数叫ω_eff可以穿越-1,不再是常数。对MP和Exp模型来说,ω_eff在演化过程中比没有粘滞的情况更接近于-1。由位力化的研究可知,粘滞还可以减缓星系结团。我们在第三章中讨论了标量挠率宇宙。标量挠率模的动力学自治方程组存在一个晚期de Sitter吸引子,相图是一族异宿轨线,这很大程度上缓解了精调问题。我们发现标量挠率宇宙的Statefinder的参数演化具有一些特别的性质,由此可以将此模型与其它模型区分。对应于动力学分析,Statefinder把参数α₁分成不同取值范围。更进一步的讨论表明,Statefinder与动力学分析相比,可以简便地区分不同模型,但是后者却能提供更多的信息。在第四章中,我们用SNeIa数据分别对粘滞Cardassian模型和标量挠率模型进行了参数拟合,给出了参数的最佳拟合值。最后,我们对本文进行了总结,并展望了未来的工作。更多还原

【Abstract】 The discovery of accelerating expansion of the universe imposes a great new challenge to the modern theory of physics and entrust a new mission to the scientific computation. Nowadays, human beings have entered into an era of precise cosmology: using the latest astronomical observations data, by the numerical method, calculate precise results and compare various theories, then give the best one. The current work explores some problems relevant to accelerating expansion of the universe by the numerical computation method and analytic method. We study two kinds of accelerating expansion theory which are viscous Cardassian universe and scalar torsion cosmology, respectively.The entire dissertation is divided into five chapters. We begin by giving some basic facts about our universe and the fundamental theory of cosmology based on the general relativity in Chapter 1. Besides, we review the classification of various accelerating cosmology models briefly. In Chapter 2, we discuss the dynamics and virialization of the viscous Cardassian models. The dynamical analysis indicates that there exists a singular curve in the phase space of viscous Cardassian model. In the viscous PL model, the equation-of-state parameter w_eff is no longer a constant and it can cross the cosmological constant divide w_∧= - 1, in contrast with same problem of the ordinary PL model. For MP and Exp models, w_eff evolves more near -1 than the case without viscosity. The virialization results show that the bulk viscosity retards the progress of collapse system. In Chapter 3 the torsion cosmology is studied. The dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology. We find that there are some typical characteristic of the evolution of statefinder parameters for the torsion cosmology that can be distinguished from the other cosmological models. The statefinder diagnostic divides the torsion parameter a₁ into differential ranges, which is in keeping with the requirement of dynamical analysis. Further discussion implies that the statefinder diagnostic has the advantage over the dynamical analysis at the simplicity, but the latter can provide more information. In Chapter 4, we fit the viscous Cardassian models and scalar torsion model to supernovae data and give the best fit values of the parameters. In the end, we give a conclusion and prospect.更多还原