作为单模引力中能量扩散的对数暗流体

中文摘要 AI 辅助

我们证明，被提出作为暗物质和暗能量单一流体统一的对数暗流体，恰好是无压力物质和具有对数能量扩散函数 $Q(a)=3A\ln a+Q_{c}$ 的耗散单模引力。这种对应在均匀背景层面是精确的，而非渐近的，并且不引入超出两种描述中已有的任何额外参数。它为对数温度 $A$ 提供了一种动力学重新解释，其起源在原始提议中未被阐明：在膨胀率范围内，$A$ 是能量从物质扩散到几何扇区的速率，即 $\dot Q=3AH$。有效流体的绝热声速为 $c_{s}^{2}=A/\rho$，其中 $\rho$ 是单模物质能量密度，并在 $a_{s}=a_{M}/2^{1/3}$ 处达到光速；此时物质能量密度消失，并在 $a_{M}$ 处改变符号，而 $a_{M}$ 正是该模型已知变为幻影时的尺度因子。由于 $\rho$ 与对数流体的焓密度 $\epsilon+P$ 一致，幻影分支是物质扇区携带负能量密度且视界熵减小的分支。最后，我们证明一个单参数饱和扩散定律消除了这些晚期病理现象，同时保留了低红移现象学。

英文摘要

We show that the logotropic dark fluid, proposed as a single-fluid unification of dark matter and dark energy, is exactly dissipative unimodular gravity with pressureless matter and the logarithmic energy diffusion function $Q(a)=3A\ln a+Q_{c}$. The correspondence is exact at the level of the homogeneous background, rather than asymptotic, and introduces no parameters beyond those already present in either description. It provides a dynamical reinterpretation of the logotropic temperature $A$, whose origin was left open in the original proposal: up to the expansion rate, $A$ is the rate at which energy is diffused from matter into the geometric sector, $\dot Q=3AH$. The adiabatic sound speed of the effective fluid is $c_{s}^{2}=A/ρ$, where $ρ$ is the unimodular matter energy density, and reaches the speed of light at $a_{s}=a_{M}/2^{1/3}$; the matter energy density then vanishes and changes sign at $a_{M}$, which is precisely the scale factor at which the model is known to become phantom. Since $ρ$ coincides with the enthalpy density $ε+P$ of the logotropic fluid, the phantom branch is the branch on which the matter sector carries negative energy density and on which the apparent horizon entropy decreases. Finally, we show that a one-parameter saturating diffusion law removes these late-time pathologies while preserving the low-redshift phenomenology.

发表机构

• Universidad Veracruzana（韦拉克鲁斯大学）
• Pontificia Universidad Católica de Valparaíso（天主教瓦帕拉索公立大学）

机构由 AI 辅助整理，请以论文原文为准。

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6 pages, no figures