A nonsingular cosmological scenario is presented in which the currently observed Riemannian configuration of spacetime originates from a primordial Weylian “stiff matter” phase driven by a geometrized inflaton-like field. In the particular case of a Friedman-Robertson-Walker line element, it is shown that an unstable original Minkowski vacuum starts to collapse adiabatically at a remote past and bounces when a minimum radius is attained. Throughout the collapsing stage, this matter-free Universe is accelerated (or “inflationary”). As in models of spontaneous quantum creation, the bouncing phase can be shown to correspond to the propagation of a Weyl instanton in an Euclideanized, classically forbidden region. In the course of the bouncing period, concurrent to the maximal deviation of the Riemannian configuration, a geometry-driven amplification mechanism operates causing the exponential increase of entropy and matter fluctuations. Once the environment temperature is always bounded, this nonadiabatical process stands for a “ Big — but finite — Bang” creation event, followed by a standard radiation-dominated era. The model describes an eternal, Friedman-like open Universe, free of many problems that hinder standard cosmology; the observed existence of a baryon excess also fits naturally within the proposed scheme.

We define relations giving all the internal quantum numbers of leptons, quarks, and hadrons from their rishon constituents. The introduction of bubbles on the rishon lines gives a bootstrap geometrical approach of quarks and leptons of any generation. It appears to limit the number of generations to 4. It is finally shown that the generalized isospin I5 of the quarks and generalized lepton number L, may be linked to the total number of rishons.