Reexamining $f(R,T)$ Gravity

We study $f(R,T)$ gravity, in which the curvature $R$ appearing in the gravitational Lagrangian is replaced by an arbitrary function of the curvature and the trace $T$ of the stress-energy tensor. We focus primarily on situations where $f$ is separable, so that $f(R,T)={f}_{1}(R)+{f}_{2}(T)$. We argue that the term ${f}_{2}(T)$ should be included in the matter Lagrangian ${\mathcal{L}}_{m}$, and therefore has no physical significance. We demonstrate explicitly how this can be done for the cases of free fields and for perfect fluids. We argue that all uses of ${f}_{2}(T)$ for cosmological modeling and all attempts to place limits on parameters describing ${f}_{2}(T)$ are misguided.