Consistent metric-affine formulation of modified gravities
After introducing the audience to metric-affine gravities, the conformal symmetry enhancement of this approach will be discussed, providing strong arguments to establish that any consistent metric-affine gravity theory has to be conformal invariant. As a byproduct, the longstanding problem stating that four degrees of freedom of the connection are not fixed by the field equations of the theory, is elegantly solved by the gauging of conformal transformations. Assuming that the gauge field associated to the conformal symmetry is dynamical, a Stueckelberg symmetry breaking is realized in a natural way, paving the way to a possible restoration of the conformal symmetry below the Plank scale. Remarkably, we show how to solve the field equation associated with the connection, making manifest the role of the gauge vector of the conformal symmetry as a possible ingredient to solve some of the current issues regarding gravitational interaction.