Are $f(R, {\rm Matter})$ theories really relevant to cosmology?

Abstract

We examine $f(R, \text{Matter})$ theories that directly couple the curvature $R$ or $R_{\mu\nu}$ 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.}