具有范德华气体和物质产生的可积宇宙模型
Integrable Cosmological Model with van der Waals Gas and Matter Creation
摘要：
本文在一个包含粒子数密度、哈勃参数和温度随时间演化的三分量自治非线性动力学系统的背景下，研究了一个含有范德瓦尔斯气体和尘埃的宇宙学模型。由于存在的对称性的模型，温度演化规律的确定（在粒子数密度方面），并与此动力系统减少到一个两个组件的一个是完全可积的。确定了全局守恒的Hamilton量，并找到了一些在低维流形上定义和守恒的特殊（第二）积分，全面研究了全局动力学的参数选择及其宇宙学意义，确定了物理意义上的参数值.
英文摘要：
A cosmological model with van der Waals gas and dust has been studied in the context of a three-component autonomous non-linear dynamical system involving the time evolution of the particle number density, the Hubble parameter and the temperature. Due to the presence of a symmetry of the model, the temperature evolution law is determined (in terms of the particle number density) and with this the dynamical system reduces to a two-component one which is fully integrable. The globally conserved Hamiltonian is identified and, in addition to it, some special (second) integrals, defined and conserved on a lower-dimensional manifold, are found. The parameter choices and their implication for the global dynamics in terms of cosmological relevance are comprehensively studied and the physically meaningful parameter values are identified.
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