Dear Michael thanks for your reply Once you introduce torsion there is this critical uncertainty about what the minimal coupling means The coupling that decouples the torsion altogether always has to be allowed  and its probably the right one There are various other fundamental problems  that its not really clear what the theory should be to describe the real world Even if you want to couple EinsteinCartan theory to ordinary electromagnetism there exists no candidate for a minimal coupling Moreover the newer more welldefined versions of the EinsteinCartan theory eg due to Stelle and West involving noncommutativity as a justification actually predict big enough phenomena and can be falsified For both claims see eg the  paper by Gibbons et al  the falsification is described in the comment about  seconds Gibbons is a senior guy who wrote important papers with Hawking and others I think its valid to say that any concrete enough version of the theory  including couplings to known types of matter  can be falsified and has been falsified So the concept is only surviving as a vague one with a wishful thinking that there could still exist a viable version of it But no such version is known  at least not a natural one Whats really missing is the motivation In string theory one can see that theres no torsion perhaps except for the Hfield a form but the Hfield doesnt have the usual normal properties of the EinsteinCartan torsion field In fact in D the Hfield may be Hodge dualized to a scalar the universal axion and such fields are naturally massive  otherwise new longrange forces would have to exist but they dont If they were not massive you would really modify the GR even at long distances and created new polarizations of gravitational waves altered the prediction for gravitational lensing and other things All these things are absent according to observations as well as string theory Moreover the very idea about the minimality of the couplings has been changed in the s by the insights of the renormalization group We no longer prefer simple couplings because they look aesthetically and subjectively simple but because we can technically prove that these couplings  and lowderivative terms  prevail at long distances This modern kind of reasoning leaves no natural room for torsion So  all the motivation is just historical in character and cant be reconciled with the modern way of organizing fields and terms in field theory and the people who defend it dont understand the last  years in theoretical physics