SSB of scale symmetry, fermion families and quintessence without the long-range force problem

Abstract

We study a scale invariant two measures theory where a dilaton field \phi has no explicit potentials. The scale transformations include a shift \phi\to\phi+const. The theory demonstrates a new mechanism for gene- ration of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, non-linear kinetic term is generated as well. The possibility of quintessence solutions are shown. As an example, for one choice of the parameters we obtain standard scaling solutions usually used in the context of the quintessential scenario. For other choice of the parameters, the theory allows a scaling solution with equation of state p_{\phi}=w\rho_{\phi} where w is restricted by -1<w<-0.82. The regime where the fermionic matter dominates (as compared to the dilatonic contribution) is analyzed. There it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles in CEF that appears to suggest a new approach to the family problem of particle physics. It is automatically achieved that for two of them, fermion masses are constants, gravitational equations are canonical and the "fifth force" is absent. For the third type of particles, a fermionic self-interaction appears as a result of SSB of scale invariance.