AI 中文总结
本文研究与最小耦合理想流体耦合的冻结引力，通过宇宙学扰动分析推导无鬼场和梯度不稳定性的条件，证明其特征性质仍成立，还推导了准静态下的有效引力耦合和引力 slip。
AI 中文摘要
冻结引力（FG）是一种phantom穿越型暗能量模型，最初是在无物质的情况下提出的。在本研究中，我们通过详细的宇宙学扰动分析，研究与理想流体最小耦合的FG，并推导无鬼场和梯度不稳定性的条件。鬼场稳定性条件是在不采用高k极限的情况下解析得到的，从而得到无鬼场的尺度范围以及（当存在时的）有限截断。在真空中已存在有限截断的分支中，我们发现物质耦合会使该截断相对于其真空值降低。此外，在高k区域，梯度稳定性条件保证冷暗物质的有效引力耦合为正。我们进一步证明，FG的两个特征性质在存在物质时仍然成立：其一，背景 sector 与扰动 sector 相互分离，即它们由独立的参数集控制，这使得FG能够实现包括phantom穿越在内的任意背景演化，同时保持稳定的扰动动力学；其二，FG的标量自由度在大尺度极限的线性阶下变为非动力学的，而在小尺度上以有限的声速传播。这种行为是否会延续到微扰论的任意高阶、从而避免潜在的强耦合问题，需要通过非线性扰动分析进一步研究。为了与大尺度结构和引力透镜观测结果建立联系，我们还推导了准静态 regime 内的有效引力耦合和引力 slip，并将结果用有效场论（EFT）参数表示。
英文摘要
Freezing gravity (FG), a phantom-crossing dark energy model, was recently proposed in the absence of matter. In this work, we study FG minimally coupled to a perfect fluid through a detailed cosmological perturbation analysis and derive the conditions for the absence of ghost and gradient instabilities. The ghost stability conditions are obtained analytically without taking the high-$k$ limit, yielding the ghost-free range of scales and a finite cutoff when it exists. In the branch where a finite cutoff is already present in vacuum, we find that matter coupling lowers it relative to its vacuum value. Moreover, in the high-$k$ regime, the gradient stability condition guarantees a positive effective gravitational coupling for cold dark matter. We further show that two characteristic properties of FG persist in the presence of matter. First, the background and perturbation sectors remain separated, in the sense that they are controlled by independent sets of parameters, allowing FG to realize arbitrary background evolutions, including phantom crossing, while maintaining stable perturbation dynamics. Second, the scalar degree of freedom of FG becomes non-dynamical in the large-scale limit at linear order, while propagating with a finite speed of sound on small scales. Whether this behavior persists to arbitrarily high orders in perturbation theory, thereby avoiding the potential strong-coupling issue, requires further investigation through a nonlinear perturbation analysis. To make contact with large-scale structure and gravitational lensing observables, we also derive the effective gravitational coupling and gravitational slip within the quasi-static regime and express our results in terms of the EFT parameters.
Comments25 pages, no figures
