In a varying-Lambda Einstein-Cartan theory, homogeneous and isotropic spacetimes can violate parity via torsion, adding a genuine new degree of freedom with Weyl curvature.
(7) This action is evidently symmetric under (5)
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Parity violating Friedmann Universes
In a varying-Lambda Einstein-Cartan theory, homogeneous and isotropic spacetimes can violate parity via torsion, adding a genuine new degree of freedom with Weyl curvature.