Why do we live in a Riemannian space time ?

Abstract

We start from the pure Einstein-Hilbert action in Metric Affine Gravity, with the orthonormal metric. We get an effective Levi-Civita Dilaton gravity theory in which the Dilaton field is related to the scaling of the gravitational coupling. When the Weyl symmetry is broken the resulting Einstein-Hilbert term is equivalent to the Levi-Civita one, using the projective invariance of the model, the non-metricity and torsion may be removed, so that we get a theory perfectly equivalent to general relativity. This may explain why low energy gravity is described by a Riemannian connection.