Our main goal here is to conduct a comparative analysis between the well-known MOND theory and a more recent model called the κ-model. An additional connection, between the κ-model and two other novel MOND-type theories, Newtonian Fractional-Dimension Gravity (NFDG) and Refracted Gravity (RG), is likewise presented. All these models are built to overtake the DM paradigm, or at least to strongly reduce the dark matter content. Whereas they rely on different formalisms, however, all four seem to suggest that the universal parameter, a0, appearing in MOND theory could intrinsically be correlated to either the sole baryonic mean mass density (RG and κ-model) and/or to the dimension of the object under consideration (NFDG and κ-model). We then confer to parameter a0 a more flexible status of multiscale parameter, as required to explain the dynamics together in galaxies and in galaxy clusters. Eventually, the conformal gravity theory (CFT) also seems to have some remote link with the κ-model, even though the first one is an extension of general relativity, and the second one is Newtonian in essence. The κ-model has been tested on a small sample of spiral galaxies and in galaxy clusters. Now, we test this model on a large sample of galaxies issued from the SPARC database.

中文翻译：

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SPARC数据库测试下的κ模型

我们这里的主要目标是对著名的 MOND 理论和更新的称为 κ 模型的模型进行比较分析。同样还提出了 κ 模型与另外两种新颖的 MOND 型理论（牛顿分数维引力 (NFDG) 和折射引力 (RG)）之间的附加联系。所有这些模型都是为了超越 DM 范式而构建的，或者至少是为了大幅减少暗物质含量。然而，尽管它们依赖于不同的形式主义，但所有四个似乎都表明 MOND 理论中出现的通用参数 a0 本质上可能与唯一的重子平均质量密度（RG 和 κ 模型）和/或维度相关所考虑的对象（NFDG 和 κ 模型）。然后，我们赋予参数 a0 一个更灵活的多尺度参数状态，以满足解释星系和星系团动力学的需要。最终，共形引力理论（CFT）似乎也与κ模型有一些遥远的联系，尽管第一个模型是广义相对论的延伸，而第二个模型本质上是牛顿模型。 κ 模型已在螺旋星系和星系团的小样本上进行了测试。现在，我们在 SPARC 数据库发布的大量星系样本上测试这个模型。