Weak Field Limit of the Nonminimally Coupled Weyl Connection Gravity

The true nature of gravity is a remarkable open problem in Gravitation. Theoretical and observational motivations open the avenue of alternative theories of gravity. One possibility resorts to nonminimal couplings and non-metricity properties of spacetime, and is dubbed as nonminimally coupled Weyl connection gravity. It has the advantage of leading to metric field equations of second order together with a constraint equation for the Weyl vector, and has well behaved space-form. We analyse this model by exploring its weak regime and its implications for astrophysics and cosmology.