相互作用暗能量的经典和圈量子宇宙学：超流暗物质与尘埃物质的动力学系统分析
Classical and Loop Quantum Cosmology of Interacting Dark Energy: A Dynamical System Analysis with Superfluid Dark Matter and Dust Matter
- Integral University（因蒂格拉尔大学）
- L. N. Gumilyov Eurasian National University（列·尼·古米廖夫欧亚国立大学）
- Symbiosis Institute of Technology, Nagpur Campus, Symbiosis International (Deemed University)（萨姆比亚斯理工学院那格浦尔校区，萨姆比亚斯国际（认定）大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
通过动力学系统分析，研究经典引力和圈量子宇宙学中相互作用暗能量与暗物质的宇宙学动力学，发现超流暗物质模型仅存在鞍点，圈量子修正消除经典吸引子。
AI中文摘要：
我们研究了经典爱因斯坦引力和圈量子宇宙学中相互作用暗能量与暗物质的宇宙学动力学。考虑了两种暗物质情景：由广义三次状态方程描述的超流暗物质和标准无压流体。暗能量组分使用广义非线性状态方程和常数状态方程建模。我们考察了两个唯象相互作用项 $Q=\alpha\dot{\rho}_m$ 和 $Q=\beta\dot{\rho}_d$，它们控制暗扇区之间的能量转移。在经典引力中，无压物质模型展现出稳定的晚期吸引子，而超流暗物质模型仅允许鞍点和非双曲临界点。将分析扩展到圈量子宇宙学，量子几何修正用非奇异的量子反弹取代了大爆炸奇点，并显著改变了相空间动力学。结果，经典无压物质模型的稳定吸引子消失，所有相互作用模型仅拥有鞍点和非双曲临界点。这些发现突显了暗物质性质和量子引力效应对相互作用暗扇区渐近演化的显著影响。
英文摘要：
We study the cosmological dynamics of interacting dark energy and dark matter in Classical Einstein Gravity and Loop Quantum Cosmology. Two dark matter scenarios are considered: superfluid dark matter described by a generalized cubic equation of state and the standard pressureless fluid. The dark energy component is modeled using both a generalized nonlinear equation of state and a constant equation of state. We examine two phenomenological interaction terms, $Q=α\dotρ_m$ and $Q=β\dotρ_d$, which govern the energy transfer between the dark sectors. In classical gravity, the pressureless matter model exhibits stable late-time attractors, whereas the superfluid dark matter model admits only saddle and non-hyperbolic critical points. Extending the analysis to Loop Quantum Cosmology, quantum geometric corrections replace the Big Bang singularity with a nonsingular quantum bounce, and significantly modify the phase-space dynamics. As a result, the stable attractors of the classical pressureless matter model disappear, and all interacting models possess only saddle and non-hyperbolic critical points. These findings highlight the significant influence of both dark matter properties and quantum gravitational effects on the asymptotic evolution of interacting dark-sectors.
