This work presents a novel approach to address the longstanding challenge posed by the rotation curves of galaxies and the associated missing mass problem. Utilizing the four-dimensional modified gravity framework of Einstein-Gauss-Bonnet (EGB), we develop a new model that integrates the concept of dark matter featuring negative mass due to the Gauss-Bonnet term. Our methodology involves using the action of EGB with boundary terms to derive the Israel junction condition, allowing the formulation of a model featuring a spherical dark halo. The mass expression of this dark halo exhibits a remarkable proportionality to the radius r at large distances, forming the basis for subsequent analyses. The model’s implications extend to the dynamics of the early Universe, where we introduce a dynamic scalar field classified as Chameleon. Posting this scalar field as the origin of dark matter effects, we establish a crucial link between the coupling constant α and the scalar field through Z2 symmetry breaking via the effective potential. This connection enables a subtle description of velocity, reminiscent of Modified Newtonian Dynamics (MOND), providing insights into the gravitational interplay and dark matter dynamics. A pivotal aspect of our study involves a particular comparison of the model’s predictions with observational data sourced from SPARC datasets. The alignment of our theoretical outcomes with empirical evidence underscores the model’s efficiency and its potential contribution to our understanding of galactic rotation dynamics.

中文翻译：

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爱因斯坦-高斯-博内特暗物质晕：负质量、旋转曲线和暗物质效应的起源


这项工作提出了一种新颖的方法来解决星系旋转曲线和相关的质量缺失问题所带来的长期挑战。利用爱因斯坦-高斯-博内特（EGB）的四维修正引力框架，我们开发了一个新模型，该模型集成了由于高斯-博内特项而具有负质量的暗物质概念。我们的方法涉及使用带有边界项的 EGB 作用来导出以色列结条件，从而可以制定具有球形暗晕的模型。这个暗晕的质量表达式在大距离上与半径 r 表现出显着的比例关系，为后续分析奠定了基础。该模型的含义延伸到早期宇宙的动力学，我们引入了一个被归类为变色龙的动态标量场。将这个标量场作为暗物质效应的起源，我们通过有效势的 Z2 对称性突破，在耦合常数 α 和标量场之间建立了关键的联系。这种联系可以对速度进行微妙的描述，让人想起修正牛顿动力学（MOND），提供对引力相互作用和暗物质动力学的见解。我们研究的一个关键方面涉及模型预测与来自 SPARC 数据集的观测数据的特定比较。我们的理论结果与经验证据的一致性强调了该模型的效率及其对我们理解星系旋转动力学的潜在贡献。