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

We study a scale-invariant two measures theory where a dilaton field φ has no explicit potentials. The scale transformations include the translation of a dilaton φ → φ + const. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, the nonlinear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. As examples, two different possibilities for the choice of the dimensionless parameters are presented where the theory permits to get interesting cosmological results. For the first choice, the theory has standard scaling solutions for φ usually used in the context of the quintessential scenario. For the second choice, the theory allows three different solutions, one of which is a scaling solution with equation of state p_φ = ωρ_φ where w is predicted to be restricted by -1 < ω < -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, the energy-momentum tensor is 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.