O ct 1 99 9 Why do we live in a Riemannian space - time ?
نویسنده
چکیده
We start from the pure Einstein-Hilbert action S = λ 2 R ⋆ 1 in Metric-Affine-Gravity, with the orthonormal metric g ab = η ab. 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 invari-ance 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.
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