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)=f1(R)+f2(T). We argue that the term f2(T) should be included in the matter Lagrangian Lm, 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 f2(T) for cosmological modeling and all attempts to place limits on parameters describing f2(T) are misguided.
@article{arxiv.1908.05306,
title = {Reexamining $f(R,T)$ gravity},
author = {Sarah B. Fisher and Eric D. Carlson},
journal= {arXiv preprint arXiv:1908.05306},
year = {2019}
}