THE GRAVITATIONAL SECTOR IN THE CONNES-LOTT FORMULATION OF THE STANDARD MODEL

We studied the Riemannian aspect and the Hilbert-Einstein gravitationa l action of the noncommutative geometry underlying the Connes-Lott con struction of the action functional of the standard model. This geometr y involves a two-sheeted, Euclidian space-time. We show that if we req uire the space of forms to be locally isotropic and the Higgs scalar t o be dynamical, then the Riemannian metrics on the two sheets of Eucli dian space-time must be identical. We also show that the distance func tion between the two sheets is determined by a single, real scalar hel d whose vacuum expectation value (VEV) sets the weak scale. (C) 1995 A merican Institute of Physics.