Kantowski-Sachs 爱因斯坦-以太标量场宇宙学模型：续篇
Kantowski-Sachs Einstein-Aether Scalar Field Cosmological Models: The Sequel
AI总结：
本文在爱因斯坦-以太引力框架中引入以太剪切与标量场的非平凡耦合，通过定性与数值稳定性分析发现幂律暴胀吸引子由各向同性变为各向异性，其稳定性依赖于剪切耦合参数 $a3$，并发现了一族仅在耦合存在时出现的渐近稳定周期轨道。
摘要：
利用 arXiv:1809.01458 中导出的常微分方程自治系统来定义演化，我们通过在未来的渐近解上引入以太场的剪切与标量场之间的非平凡耦合，进一步研究了爱因斯坦-以太引力框架内的一类宇宙学模型。随后，我们对新的平衡点集进行了定性和数值稳定性分析，并首要地确定：在这种耦合存在的情况下，膨胀型幂律暴胀吸引子变得各向异性，而非各向同性。进一步表明，该解的稳定性依赖于剪切耦合参数 $a3$ 的值。我们还发现了一族渐近稳定的周期轨道，它们存在于 Bianchi I 不变集内特定的参数值范围内，并且在以太场与标量场之间不存在耦合时消失。
英文摘要：
Utilizing the autonomous system of ordinary differential equations derived in arXiv:1809.01458 to define the evolution, we further investigate a class of cosmological models within an Einstein-aether gravitational framework by introducing a non-trivial coupling between the shear of the aether field to the scalar field on the future asymptotic solution. We subsequently conduct qualitative and numerical stability analysis on the new set of equilibrium points and paramountly determine that the expansionary power-law inflationary attractor becomes anisotropic rather than isotropic in the presence of such a coupling. It is further shown that the stability of this solution is dependent on the value of the shear coupling parameter $a3$. We also discover a family of asymptotically stable periodic orbits which exist for a particular range of parameter values within the Bianchi I invariant set and vanish in the absence of coupling between the aether field and the scalar field.
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