Weyl-Cartan-Weitzenb\"{o}ck gravity as a generalization of teleparallel gravity

Understand

We consider a gravitational model in a Weyl-Cartan space-time, in which the Weitzenb\"{o}ck condition of the vanishing of the sum of the curvature and torsion scalar is also imposed.

• Moreover, a kinetic term for the torsion is also included in the gravitational action.
• The field equations of the model are obtained from a Hilbert-Einstein type variational principle, and they lead to a complete description of the gravitational field in terms of two fields, the Weyl vector and the torsion, respectively, defined in a curved background.
• The cosmological applications of the model are investigated for a particular choice of the free parameters in which the torsion vector is proportional to the Weyl vector.