Weyl Geometry as Characterization of Space-Time

TL;DR

This paper explores a reformulation of Einstein's gravity using Weyl geometry, introducing gauge symmetry and potential cosmological implications, aiming to deepen the understanding of space-time structure.

Contribution

It presents a Weyl geometric reformulation of gravity with gauge symmetry, analyzing its implications for test particles and cosmology.

Findings

Weyl geometry modifies test particle trajectories.

The theory introduces a gauge symmetry for geometrical fields.

Potential to describe cosmological observations with a scalar field.

Abstract

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.