We examine f(R, Matter) theories that directly couple the curvature R or R _μν with the matter sector in the action, in addition to the universal coupling. We argue that if the matter sector includes the Standard Model (SM), such theories are either inconsistent or already excluded by experiments unless they are a rewriting of f(R) gravity or general relativity. If these theories genuinely couple the SM to curvature, they suffer from the presence of ghost states at energies within their domain of application for cosmological purposes. Therefore, we raise questions about their relevance to cosmology. Moreover, if such theories do not include the SM, they should just be seen as scalar-tensor, vector-tensor, …, theories, depending on the additional degrees of freedom. They should thus be studied accordingly.

中文翻译：

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f(R, Matter) 理论真的与宇宙学相关吗？


我们研究了 f(R, Matter) 理论，除了通用耦合之外，还直接将曲率 R 或 R _μν 与作用中的物质扇区耦合。我们认为，如果物质部门包括标准模型（SM），那么这些理论要么不一致，要么已经被实验排除，除非它们是 f(R) 引力或广义相对论的重写。如果这些理论真正将 SM 与曲率耦合起来，那么它们在宇宙学目的应用范围内的能量上就会遭受鬼态的存在。因此，我们对它们与宇宙学的相关性提出疑问。此外，如果此类理论不包括 SM，则它们应该仅被视为标量张量、矢量张量……理论，具体取决于附加自由度。因此应该对它们进行相应的研究。