Variational principle for general relativity with torsion and non-metricity

The variation of the field action with the scalar Lagrangian density $\text{?g}\text{R}$ is calculated with respect to the metric, torsion and non-metricity. When the non-metricity vanishes, the variation reduces to the U₄ theory of gravitation when a relativistic matter Lagrangian with minimal coupling is included.