Conformal symmetry in modified gravities
A longstanding problem of the metric-affine approach to gravity is the fact that four degrees of freedom of the connection are not fixed by the field equations of the theory. This is a consequence of an underlying invariance of a large class of gravity theories usually referred to as projective symmetry. In this talk, we propose a solution to this problem by revisiting and generalizing the interpretation of the projective symmetry as a gauging of the conformal transformations. Furthermore, we provide strong arguments to establish that any consistent metric-affine gravity theory has to be conformal invariant. 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 to 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.
the 20th of October 2022, 14:30