The trace of the trace of the energy–momentum tensor-dependent Einstein’s field equations

Abstract

Abstract The f(R, T) gravity field equations depend generically on both the Ricci scalar R and trace of the energy–momentum tensor T. Within the assumption of perfect fluids, the theory carries an arbitrariness regarding the choice of the matter lagrangian density $${\mathcal {L}}$$ L , not uniquely defined. Such an arbitrariness can be evaded by working with the trace of the theory field equations. From such an equation, one can obtain a form for $${\mathcal {L}}$$ L , which does not carry the arbitrariness. The obtained form for $${\mathcal {L}}$$ L shows that the f(R, T) gravity is unimodular. A new version of the theory is, therefore, presented and forthcoming applications are expected.