On the physical interpretation of non-metricity in Brans-Dicke gravity

Abstract

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.

9 pages. I added some comments on the role of a non-holonomic basis and minor corrections in the notation. Also the title was modified. Version accepted for International Journal of Geometric Methods in Modern Physics (IJGMMP)

References in corpus (8)

• The (pseudo)issue of the conformal frame revisited
• Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein Frames
• Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints
• Extended disformal approach in the scenario of Rainbow Gravity
• Cosmological models in Weyl geometrical scalar-tensor theory
• Weyl relativity: A novel approach to Weyl's ideas
• The unexpected resurgence of Weyl geometry in late 20-th century physics
• On the embedding of Weyl manifolds

Cited by in corpus (3)

• Underdetermination in Classic and Modern Tests of General Relativity
• A generalized Weyl structure with arbitrary non-metricity
• On the Cauchy Problem for Weyl-Geometric Scalar-Tensor Theories of Gravity