In this work, we examine in depth the physical aspects of the archaic universe described by Euclidean 5-sphere geometry, by using Projective Relativity techniques. We hypothesize that the expansion of the Universe was "ignited" by primordial R processes, and that the big bang consisted of a spatially extended nucleation process which took place at the end of a pre-cosmic phase, characterized by the evolution parameter x 0 . This parameter, which can be considered a quantum precursor of ordinary physical time, is a coordinate of Euclidean 5-sphere metrics. It is so possible to avoid many of the difficulties with standard model and to get rid of ad hoc assumptions. A complete solution to Projective General Relativity (PGR) equations is provided, so as to establish univocal relations between the scale factor R(τ ) and cosmic time τ . In this way, the physics and geometry of the cosmological model are specified completely.