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.

• Received 19 August 2019

DOI:https://doi.org/10.1103/PhysRevD.100.064059