Progress in Einstein-Cartan gravity

It is well-known that the gravitational force can be obtained by gauging the Lorentz group, which puts gravity on the same footing as the Standard Model fields. The resulting theory - Einstein-Cartan gravity - has several crucial advantages. I will overview the construction of the Weyl-invariant version of this theory and discuss its applications in particle physics and cosmology, in particular for inflation and the strong CP problem.