AI 中文总结
本文研究超流体暗物质与玻色-爱因斯坦凝聚暗物质的关系，通过RAQUAL理论的低加速度极限建立联系，发现二者相互作用等价但动能部分不等价，明确了可转移的理论性质。
AI 中文摘要
受共同的凝聚态灵感以及在星系尺度上协调类MOND现象学与更大尺度上粒子暗物质的共同目标驱动，我们研究超流体暗物质（SFDM）与玻色-爱因斯坦凝聚暗物质（BECDM）之间的关系。由于SFDM在牛顿框架下构建，而BECDM完全是相对论性的，我们首先证明，SFDM的类MOND表述是爱因斯坦框架下相对论二次拉格朗日（RAQUAL）理论的牛顿低加速度极限。随后，我们将其协变相互作用部分变换到乔丹框架，并与BECDM进行比较。SFDM的声子-重子相互作用对应于BECDM与爱因斯坦张量的导数耦合，辅以与里奇标量的小非最小耦合。因此，在爱因斯坦-希尔伯特项的线性扰动下，相互作用部分是等价的，但它们的动能部分仍不等价：BECDM的标准二次动能项无法映射到SFDM所需的非解析动能项。因此，这两个模型相关但动力学上不等价。该映射为SFDM的相互作用提供了协变解释，并阐明了哪些理论性质可以在两个框架之间转移。
英文摘要
Motivated by their common condensed-matter inspiration and their shared aim of reconciling MOND-like phenomenology on galactic scales with particle dark matter on larger scales, we investigate the relation between Superfluid Dark Matter (SFDM) and Bose--Einstein Condensate Dark Matter (BECDM). Since SFDM is formulated in the Newtonian regime whereas BECDM is fully relativistic, we first show that the MONDian formulation of SFDM arises as the Newtonian, low-acceleration limit of a Relativistic AQUAdratic Lagrangian (RAQUAL) theory in the Einstein frame. We then transform its covariant interaction sector to the Jordan frame and compare it with BECDM. The phonon--baryon interaction of SFDM maps onto the BECDM derivative coupling to the Einstein tensor, supplemented by a small non-minimal coupling to the Ricci scalar. The interaction sectors are therefore equivalent up to a linear perturbation of the Einstein--Hilbert term. Their kinetic sectors, however, remain inequivalent: the standard quadratic kinetic term of BECDM cannot be mapped onto the non-analytic kinetic term required by SFDM. The two models are consequently related but not dynamically equivalent. This mapping provides a covariant interpretation of the SFDM interaction and clarifies which theoretical properties can be transferred between the two frameworks.
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