A Is gravity simply an interaction in the gauge theory of gravity?

[vanhees71]

Yes, it is about the global topology. I know how you could get a torus or hole topology in GR. How could you do that in the Einstein Cartan theory?

I, for one, have no hostility towards it. In fact, I would be very interested in some experimental results (in matter of course) that could distinguish them. I think there is a good chance that the eventual classical limit of a correct quantum gravity theory will be the Einstein Cartan theory rather than GR.

However, I don’t see any way to get a hole or torus topology in the gauge theory. I don’t think that is a problem because we don’t have any experimental confirmation of non-trivial topologies. It is merely a difference with GR. It is not the most important difference, but it is a legitimate difference as far as I can tell.

I must admit that I don't know enough about the global topology in GR nor in Einstein Cartan theory. Do you have a reference concerning the torus or hole in GR?

From an experimental point of view, of course, almost everything concerning GR is in the astronomical context, i.e., dealing with macroscopic matter, partially "under extreme conditions" and all observations are "local", and that's why for sure it is hard to imagine that we'll be ever able to empirically learn about the global topology of the universe. Of course, the cosmological "concordance model", i.e., the $\Lambda \text{CDM}$ model is pretty convincing and amazingly successful in the recent years particularly with the more and more precise measurements of the CMBR fluctuations, including recently again the polarization and the redshift-distance relationship/"Hubble Law" via the establishment of "standard candles" (like Supernovae of Type Ia). A caveat is that more recently there are again some inconsistencies between different determinations of the Hubble constant and its evolution. Other tests of GR vs. alternative theories made also a lot of progress, e.g., pulsar timing and the analysis of black-hole mergers and, even more interesting, neutron-star mergers ("kilonovae"), etc.

I think it's very difficult to check for torsion as predicted by the gauge approach leading to an Einstein-Cartan manifold in relation to spin since according to this theory it's only observable in the medium, and the macroscopic bodies we can test the theories of gravity are "spin saturated" many-body systems like neutron stars. FAPP they are well described on the classical level with hydrodynamics (or magneto hydrodynamics as the just yesterday published paper by my colleagues in Frankfurt on the jet of the black hole in M87 in Nature Astronomy [1]), and there you expect the usual torsion free connection. According to the theory, torsion is also not observable outside of the matter, i.e., it cannot be observed by the motion of objects under influence of their mutual gravitational interaction, i.e., a high-precision method like pulsar timing is not expected to observe torsion.