A generalized Weyl structure with arbitrary non-metricity

Abstract

A Weyl structure is usually defined by an equivalence class of pairs $(\mathbf{g},\mathbf{\omega })$ related by Weyl transformations, which preserve the relation $\nabla \mathbf{g}=\mathbf{\omega }\otimes \mathbf{g}$, where $\mathbf{g}$ and $\mathbf{\omega }$ denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection ${\Gamma }_{\mathbf{\omega }}$, which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric.

9 pages, updated to match published version, some discussions extended

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• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Dark energy from a geometrical gauge scalar-tensor theory of gravity
• The role of longitudinal polarizations in Horndeski and macroscopic gravity: Introducing gravitational plasmas