On the physical interpretation of non-metricity in Brans-Dicke gravity
  Brans-Dicke theory is described by an action that allows the so called frame transformation, which replaces the non-minimal coupling between the scalar field and the curvature by a coupling between the scalar field and matter fields. In this paper, we describe how the viewpoint that they are physically equivalent has a geometrical counterpart in the framework of Weyl integrable geometry. This way, Dicke's interpretation in terms of running units is a physical manifestation of the non-metricity tensor. 
Iarley P. Lobo
gr-qc