On Scalar Cosmological Perturbations in Non-Minimally Coupled Weyl Connection Gravity

We analyze a theory with non-minimal matter-curvature coupling, considering non-metricity properties with a Weyl connection. This model has the advantage of an extra force term which can mimic dark matter and dark energy, and simultaneously follow Weyl's idea to unify gravity and electromagnetism. Indeed, Schwarzschild-like and Reissner-Nordstrom-like black hole solutions exist in this model, leading to new features, such as an additional horizon, due to the non-metricity vector. We derive the cosmological field equations, considering a minimal coupling, and discuss preliminary results on the scalar cosmological perturbations in this model.