AI 中文总结
本文在f(𝒯)引力中研究Xu型广义全息里奇暗能量的动力学，分析其稳定性、相空间吸引子等，模型符合观测，后期加速稳健，后续将开展多观测数据结合的约束研究。
AI 中文摘要
本文研究嵌入幂律f(𝒯)=α𝒯+β𝒯ᵗᵐ的teleparallel引力中，Xu型广义全息里奇暗能量（GHRDE）的宇宙学动力学，其由依赖哈勃参数的减速定律q=b−ν/H驱动。该减速定律给出精确闭式哈勃函数H(z)，可插值早期减速相与渐近de Sitter regime，使所有宇宙学诊断量能表示为红移的显式解析函数。当前减速参数q₀=−0.60、转变红移zₜ=1.0与当前观测估计一致；GHRDE的状态方程参数ω_G,0=−0.81处于Quintessence带，有效状态方程单调演化至−1且无phantom crossing。几何Statefinder对将模型定位于r−s平面的Quintessence区域，明显偏离ΛCDM不动点。相空间分析显示存在带严格负本征值的稳定节点de Sitter吸引子，确保一般初始条件下后期加速稳健；所考虑红移范围内满足零能、弱能与主导能条件，低红移处违反强能条件，符合加速宇宙预期。本文后续工作将结合宇宙计时数据、Pantheon+超新星与重子声学振荡测量的观测约束方法。
英文摘要
The cosmological dynamics of generalized holographic Ricci dark energy (GHRDE) of Xu type, embedded within power-law $f(\mathcal{T})=α\mathcal{T}+β\mathcal{T}^{m}$ teleparallel gravity and driven by the Hubble-parameter-dependent deceleration law $q=b-ν/H$, are investigated. The deceleration law yields an exact closed-form Hubble function $H(z)$ that interpolates between an early decelerating phase and an asymptotic de~Sitter regime, enabling all cosmological diagnostics to be expressed as explicit analytical functions of redshift. The present-day deceleration parameter $q_{0}=-0.60$ and transition redshift $z_{t}=1.0$ are consistent with current observational estimates. The GHRDE equation-of-state parameter $ω_{G,0}=-0.81$ lies within the quintessence band, and the effective equation of state evolves monotonically toward $-1$ without phantom crossing. The geometrical statefinder pair locates the model in the quintessence region of the $r$--$s$ plane, clearly displaced from the $Λ$CDM fixed point. A phase-space analysis reveals a stable-node de~Sitter attractor with strictly negative eigenvalues, guaranteeing robust late-time acceleration for generic initial conditions. The null, weak, and dominant energy conditions are satisfied throughout the redshift range considered, while the strong energy condition is violated at low redshift, as expected for an accelerating Universe. An observational constraint methodology combining cosmic chronometer data, Pantheon$+$ supernovae, and baryon acoustic oscillation measurements is outlined as the natural continuation of this work.
Comments33 pages, 12 figures, 2 tables. Investigates generalized holographic Ricci dark energy (GHRDE) of Xu type in power-law f(T) teleparallel gravity with deceleration law q=b-nu/H. Derives exact closed-form Hubble function; presents statefinder, stability, phase-space, and energy condition analyses
