一类无旋、非线性传递$G_{2}$宇宙学II的动力学平衡态：具有一个超曲面正交Killing矢量场的模型
Dynamical Equilibrium States of a Class of Irrotational Non-Orthogonally Transitive $G_{2}$ Cosmologies II: Models With One Hypersurface-Orthogonal Killing Vector Field
摘要：
考虑一类非齐次自相似宇宙模型，其中理想流体流与三参数相似群的轨道相切。我们限制的相似性组具有阿贝尔$G_{2}$，和一个超曲面正交Killing向量场，我们限制的流体流是正交的阿贝尔$G_{2}$的轨道。由于相似群的存在，模型的时间演化被迫服从幂律，爱因斯坦场方程简化为一个三维自治常微分方程系统，定性分析该系统以确定模型的空间结构。证明了两类行为良好的模型的存在。其中第一个是渐近空间均匀和物质为主，第二个是真空为主，无论是渐近空间均匀或加速度为主，在大的空间距离。
英文摘要：
We consider a class of inhomogeneous self-similar cosmological models in which the perfect fluid flow is tangential to the orbits of a three-parameter similarity group. We restrict the similarity group to possess both an Abelian $G_{2}$, and a single hypersurface orthogonal Killing vector field, and we restrict the fluid flow to be orthogonal to the orbits of the Abelian $G_{2}$. The temporal evolution of the models is forced to be power law, due to the similarity group, and the Einstein field equations reduce to a three-dimensional autonomous system of ordinary differential equations which is qualitatively analysed in order to determine the spatial structure of the models. The existence of two classes of well-behaved models is demonstrated. The first of these is asymptotically spatially homogeneous and matter dominated, and the second is vacuum dominated and either asymptotically spatially homogeneous or acceleration dominated, at large spatial distances.
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