Consistency of universally nonminimally coupled $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ theories

We discuss the consistency of a recently proposed class of theories described by an arbitrary function of the Ricci scalar, the trace of the energy-momentum tensor, and the contraction of the Ricci tensor with the energy-momentum tensor. We briefly discuss the limitations of including the energy-momentum tensor in the action, as it is a nonfundamental quantity but a quantity that should be derived from the action. The fact that theories containing nonlinear contractions of the Ricci tensor usually lead to the presence of pathologies associated with higher-order equations of motion will be shown to constrain the stability of this class of theories. We provide a general framework and show that the conformal and nonminimal couplings to the matter fields usually lead to higher-order equations of motion. To illustrate such limitations, we explicitly study the cases of a canonical scalar field, a $K$-essence field, and a massive vector field, whereas for the scalar field cases, it is possible to find healthy theories, and for the vector field case, the presence of instabilities is unavoidable.