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.

中文翻译：

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康托夫斯基-萨克斯爱因斯坦-以太标量场宇宙学模型：续集

利用 arXiv:1809.01458 中导出的常微分方程自治系统来定义演化，我们通过在以太场的剪切与标量之间引入非平凡的耦合，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关于未来渐近解的领域。我们随后对一组新的平衡点进行定性和数值稳定性分析，并最重要的是确定膨胀幂律膨胀吸引子在这种耦合的存在下变为各向异性而不是各向同性。进一步表明，该解的稳定性取决于剪切耦合参数 $a3$ 的值。