Observational constraints on Weyl geometric gravity from the SPARC galactic rotation curves database

Weyl geometry is an interesting, non-metric, extension of Riemann geometry, which fully implements the fundamental requirement of the conformal invariance of the physical laws. Gravitational models constructed from the square of the Weyl geometric scalar and from the strength of the Weyl vector can be linearized by introducing a scalar degree of freedom. The corresponding theory has an exact, static spherically symmetric solution, which can provide an effective description of the galactic rotation curves, without the need of introducing the elusive dark matter. We perform an observational test of the Weyl geometric dark matter model, by comparing the theoretical predictions of the rotation curves velocity with the observational data of the SPARC database. Our results show that the Weyl geometric gravity model can provide an acceptable description of the galactic dynamics, and of the properties of the rotation curves.