Particle Physics and Symmetries in Noncommutative Geometry

In the context of the spectral action and the noncommutative geometry approach to the physical fundamental interactions, we extend the standard model of particle physics introducing a model based on a larger symmetry in the attempt to obtain a new scalar field, bringing the Higgs mass in the vicinity of 126~GeV and to cure the instability problem of the electroweak vacuum. We also investigate whether inclusion of dimension six terms in the Standard Model Lagrangian or gravitational contributions may cause the unification of the gauge coupling constants at high energy scale.