Inflation and Weyl symmetry in extended theories of gravity: A new take on gauging Weyl symmetry

Abstract

In this thesis we study both classical and quantum properties of a gauge realisation of Weyl symmetry, achieved by endowing the space-time manifold with a torsional connection. Some component of torsion can then act as a gauge connection, thus compensating the local transformations of the metric tensor and the fields. This leads to a rather generic physical theory, described in chapter 2, which features a dilaton and a vector field on top of the usual particle content of the standard model. We then study a possible mechanism that spontaneous breaks conformal symmetry, showing that cosmological inflation can be described in such a framework. The resulting model has notable features and agrees with inflationary observables in a wide range of the parameter space. In chapter 4 we discuss detection of torsion by means of gravitational waves detectors, which is within range of experimental approach once the space based gravitational detectors will be online. Finally in chapter 5 we address the conformal anomaly and present first evidence that the extended Ward identity, which take into account the additional vector field, hold in a perturbative dimensional renormalization scheme, even when anomalous contributions are generated in the energy momentum tensor trace.