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 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.