AI 中文总结
该研究在双流体宇宙学框架下，构建了奇异闭合守恒关系，推导了修正利纳德方程，明确了非零α族的奇异性，为区分引力模型的作用量预测与闭合伪影提供了诊断方法。
AI 中文摘要
在多流体物质型引力中，比安基恒等式约束总有效应力张量的散度，但本身并不确定其组成部分对应的流；这些流仅在确定了离壳物质作用量与方程，或补充了唯象闭合关系后才能被选取。我们明确了该区别，并研究了受尺度无关EMSG启发的空间平直双流体背景。该案例研究结合了代数理想流体设定、收缩海森贡献为零的条件，以及总常规部分与修正部分分别守恒的要求。由于此处的两个假设均非源自具体的离壳流体作用量，所得系统是有效背景闭合关系，而非微观EMSG模型。对于不等的物态方程（EoS）和所有α≠0的情况，该闭合关系会产生Barrow-Clifton系统，其传递系数依赖于(w₁,w₂)但不依赖于α，因此非零α族是奇异的：当α→0时，其极限不会回到无耦合的广义相对论（GR）守恒律。我们求解了两个密度本征模，并推导了对应于哈勃参数H的修正利纳德方程。我们还证明，对于所有有限的w₁≠w₂，控制密度重构映射秩损失的判别式严格为正，因此每个真正的二次情况都有两个不同的实秩简并耦合。精确真空和刚性流体族说明了模态抵消现象。当当前常规密度为正时，在明确分析的参数范围内，两者均保持正的区间通常在有限端点处终止。这些结果为区分多流体物质型引力中作用量层级预测与闭合关系伪影提供了一致性诊断；但并未建立一个观测上可行的EMSG模型。
英文摘要
In multi-fluid, matter-type gravity, the Bianchi identity constrains the divergence of the total effective stress tensor but does not, by itself, determine the currents assigned to its constituent sectors. Those currents are selected only after the off-shell matter action and equations, or an additional phenomenological closure, have been specified. We formulate this distinction and examine a spatially flat two-fluid background inspired by scale-independent EMSG. The case study combines an algebraic perfect-fluid prescription with a vanishing contracted-Hessian contribution, together with separate conservation of the total conventional and modification sectors. Because neither assumption is derived here from a concrete off-shell fluid action, the resulting system is an effective background closure rather than a microscopic EMSG model. For unequal EoS and every $α\ne0$, the closure yields a Barrow-Clifton system whose transfer coefficients depend on $(w_1,w_2)$ but not on $α$. Hence the nonzero-$α$ family is singular: its $α\to0$ limit does not recover the uncoupled GR conservation laws. We solve the two density eigenmodes and derive the associated modified Liénard equation for $H$. We also prove that the discriminant governing rank loss of the density-reconstruction map is strictly positive for every finite $w_1\ne w_2$. Thus each genuinely quadratic case has two distinct real rank-degenerate couplings. Exact vacuum and stiff-fluid families illustrate modal cancellation. When today's conventional densities are positive, the intervals on which both remain positive generally terminate at finite endpoints in the parameter ranges analyzed explicitly. These results provide a consistency diagnostic for separating action-level predictions from closure artifacts in multi-fluid, matter-type gravity; they do not establish an observationally viable EMSG model.
Comments19 pages, 2 figures
