标题： Barrow 全息暗能量在$f(Q,L_{m})$引力中的研究：从动力系统视角出发 显示英文标题

标题： Barrow Holographic Dark Energy in $f(Q,L_{m})$ gravity: A dynamical system perspective

摘要： 在这项工作中，我们在 $f(Q,L_{m})$ 引力框架内研究了 Barrow 全息暗能量（BADE）模型的宇宙学意义，特别是考虑了 $f(Q,L_{m})=\alpha Q+\beta L_{m}$ 模型。通过非相互作用和相互作用场景的动力系统方法，我们确定了对应于宇宙不同演化阶段的关键点，包括物质主导、辐射主导以及暗能量驱动的加速膨胀。 我们的分析揭示了在非相互作用情况下存在两个稳定的临界点，在相互作用情况下存在三个稳定的临界点，每个点都表明向以BADE为主的稳定阶段过渡。相图清楚地展示了宇宙动力学向这些稳定点的演化过程。 在这些稳定点上，减速参数为负值，与加速膨胀一致，而状态方程参数表明BADE表现为一种暗能量成分。这些发现突显了BADE模型作为解释 $f(Q, L_{m})$ 引力中晚期宇宙加速的有效理论的优势，并为暗能量-物质相互作用的宇宙发展提供了新的视角。 显示英文摘要

摘要： In this work, we investigate the cosmological implications of the Barrow Holographic Dark Energy (BADE) model within the framework of $f(Q,L_{m})$ gravity, specifically considering the model $f(Q,L_{m})=\alpha Q+\beta L_{m}$. Using a dynamical system approach for both non-interacting and interacting scenarios, we identify critical points corresponding to different phases of the Universe's evolution, including matter domination, radiation domination and dark energy-driven accelerated expansion. Our analysis reveals two stable critical points in the non-interacting case and three stable critical points in the interacting case, each indicating a transition to a stable phase dominated by BADE. The phase plots clearly demonstrate the evolution of the Universe's dynamics toward these stable points. At these stable points, the deceleration parameter is negative, consistent with accelerated expansion and the equation of state parameter suggests that BADE behaves as a dark energy component. These findings highlight the BADE model's strength as a viable explanation for the Universe's late-time acceleration inside $f(Q, L_{m})$ gravity, and they provide novel perspectives on the cosmic development of dark energy-matter interactions.