We discuss the advantages of using metric theories of gravity with curvature–matter couplings in order to construct a relativistic generalization of the simplest version of Modified Newtonian Dynamics (MOND), where Tully–Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless particles (photons). These constructions can be divided into local and non-local metric theories of gravity with curvature–matter couplings. Using the simplest two local constructions in an FLRW universe for dust, we show that there is no need for the introduction of dark matter and dark energy components into the Friedmann equation in order to account for type Ia supernovae observations of an accelerated universe at the present epoch.

中文翻译：

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使用具有曲率-物质耦合的引力度量理论的 MOND 的非真空相对论扩展及其在没有暗成分的宇宙加速膨胀中的应用

我们讨论了使用具有曲率-物质耦合的引力度量理论的优势，以构建最简单版本的修正牛顿动力学 (MOND) 的相对论推广，其中 Tully-Fisher 标度适用于各种天体物理对象。我们表明，这些建议在大质量和无质量粒子（光子）轨迹的最弱扰动阶下是有效的。这些结构可以分为具有曲率-物质耦合的局部和非局部度量重力理论。使用 FLRW 宇宙中最简单的两个局部结构来计算尘埃，我们表明不需要在弗里德曼方程中引入暗物质和暗能量成分来解释目前对加速宇宙的 Ia 型超新星观测时代。