  In this work, we examine in depth the cosmological physical aspects of the
archaic universe described by Euclidean 5-sphere geometry. (see Int. Jour. of
Theor., Phys 2009, 48:1003-1018). We hypothesize 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 x0. This parameter,
which can be considered a quantum precursor of ordinary physical time, is a
coordinate of Euclidean 5-sphere metrics. We must now examine what the
privileged role of the x0 axis consists in. The big bang is a sort of
nucleation of matter and fields by vacuum; to try to understand it we must
therefore make some assumptions regarding a pre-cosmic state of matter and
energy. The introduction of an evolution parameter such as x0 which can be
extended to pre-big bang situations is absolutely necessary if we are to define
any pre-cosmic dynamics. A generalized Bekenstein relation is here proposed for
archaic Universe. A complete solution to Projective General Relativity (PGR)
equations in the De Sitter Universe is provided, so as to establish univocal
relations between the scale factor R(tau) and cosmic time tau. In this way, the
physics and geometry of the cosmological model are specified completely.
