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

TL;DR

This paper explores the geometric and physical significance of non-metricity in Brans-Dicke gravity, linking frame transformations to Weyl integrable geometry and interpreting non-metricity as running units.

Contribution

It provides a geometric interpretation of non-metricity in Brans-Dicke theory using Weyl integrable geometry, connecting physical and mathematical perspectives.

Findings

Non-metricity corresponds to running units in physical interpretation.

Frame transformations relate to Weyl geometry structures.

Non-metricity has a clear physical meaning in the context of Brans-Dicke theory.

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.