Weyl type $f(Q,T)$ gravity, and its cosmological implications

Understand

We consider an $f(Q,T)$ type gravity model in which the scalar non-metricity $Q_{\alpha \mu \nu}$ of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $w_{\mu}$.

• The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier.
• The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier.
• The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum.