AI 中文总结
该研究构建含正压流体与全息暗能量的宇宙学模型，解析描述幻影边界穿越，确定熵标度维数表达式，验证结果与标准宇宙学早期阶段一致，还需幻影区域额外暗能量熵以满足热力学定律。
AI 中文摘要
我们考虑一个空间平坦的宇宙学模型，包含非相互作用的正压流体和以未来事件视界为红外截断的全息暗能量。我们通过视界半径的光滑正函数参数化视界熵与Bekenstein-Hawking形式的偏差。我们将背景演化简化为闭合自治系统，并解析描述幻影边界w=-1的穿越过程。对于增长慢于半径四次方的熵，穿越是唯一的，发生在事件视界半径的极值处，从 quintessence 区域进入幻影区域。此时穿越处的局部Chevallier-Polarski-Linder系数w_{a,loc}为正，其符号直接约束视界尺度的局部熵标度维数。穿越运动学给出局部熵标度维数的精确表达式，而Barrow-Tsallis熵中尺度依赖Barrow指数的局部规定可实现熵函数的解析重构。早期渐近行为与标准物质和辐射主导时代一致，而事件视界一致性准则选择物理上可接受的晚期轨迹，这些轨迹导致de Sitter态、III型或大撕裂奇点，或当δ=1时导致加速幂律膨胀。解析结果通过数值示例说明。在总熵的采用分解下，热力学广义第二定律进一步要求幻影区域存在额外的暗能量熵：吉布斯关系隐含的平衡熵演化在穿越处已不满足该定律，而纯正压绝热的扰动描述也在此处失效。
英文摘要
We consider a spatially flat cosmological model containing a noninteracting barotropic fluid and holographic dark energy with the future event horizon as the infrared cutoff. We parametrize the deviation of the horizon entropy from the Bekenstein--Hawking form by a smooth positive function of the horizon radius. We reduce the background evolution to a closed autonomous system and analytically describe the crossing of the phantom divide, $w=-1$. For entropies growing more slowly than the fourth power of the radius, the crossing is unique, occurs at an extremum of the event-horizon radius, and proceeds from the quintessence regime into the phantom regime. The local Chevallier-Polarski-Linder coefficient $w_{a,\mathrm{loc}}$ at the crossing is then positive, and its sign directly constrains the local entropy-scaling dimension at the horizon scale. The crossing kinematics yields an exact expression for the local entropy-scaling dimension, and a local prescription for the scale-dependent Barrow exponent in the Barrow--Tsallis entropy enables an analytic reconstruction of the entropy function. The early-time asymptotics remain consistent with the standard matter- and radiation-dominated eras, while the event-horizon consistency criterion selects physically admissible late-time trajectories leading to de Sitter states, to Type III or Big Rip singularities, or, for $δ=1$, to accelerated power-law expansion. The analytic results are illustrated numerically. Within the adopted decomposition of the total entropy, the generalized second law of thermodynamics further requires an additional dark-energy entropy in the phantom regime: the equilibrium entropy evolution implied by the Gibbs relation fails to satisfy the law already at the crossing, where the purely barotropic adiabatic description of perturbations also breaks down.
Comments22 pages, 2 figures
