Blackforest asked about an interesting paper recently posted by G.F.R. Ellis, that MTd2 spotted and added to our bibliography. I hope we can have some discussion of the Ellis paper. Unimodular gravity is a variant of the usual GR which is restricted to metrics which do not feel "vacuum energy". In other respects it reproduces all the usual GR behavior. So it is a way of avoiding the fact that Quantum Field Theory (developed on flat Minkowski space with no gravity, thus in a very different context) predicts an embarrassingly huge vacuum energy which we do not observe. In unimodular GR this energy (if it existed) would have no effect. Ellis "trace-free" is, he says, essentially the same as unimodular GR. So the good news is it does not suffer from the absurd QFT vacuum energy. But then what happens in the supposed inflation era when one WANTS an inflaton field to behave somewhat like this high vacuum energy? Ellis addresses this question.