  In this paper we construct a physical modelization of the universe expansion.
The universe then reduces to a Riemannian space $0.2cm$ $(B(O,R(t)),g_t)$,
where $R(t) \sim t$ for $t \gg $0, and $g_t$ is a time - dependent Riemannian
metric which reflects and characterizes the dynamical matter - energy
distribution $E_t(X)$ on $B(O,R(t))$ according to the Mach - Einstein
principle. Our model allows us to resolve several major problems of Physics. It
is consistent in the sense that all Newtonian and classical physical laws are
valid as particular cases in classical situations. Moreover, our model permits
to recover some confirmed principles and postulates such as the famous
Einstein's relationship $ E = mc^2$ and to specify some approximate results of
modern Physics. After showing, rigorously, the deficiency of the second part of
the special relativity second postulate and after specifying the role of the
wave quantum Mechanics and the quantum Statistics, we adapt the Einstein's
general relativity theory and the (Einstein - de Sitter - Friedmann)
homogeneous isotropic cosmology to our setting. This readaptation allows us to
determine the age, the size and the total energy of our universe and to prove
that only the total energy E, the electromagnetic constant $ke^2$ and the speed
of light c are time - independent universal constants. The other fundamental
constants of Physics (such as G,$\bar{h}$, $K_B 0.05cm T$, $\alpha$...) are
indeed time - dependent and naturally related to the previous ones.
Consequently, we realize the unification of all Physics' domains The expanding
universe is so reduced to four basic elements (E, c, $ke^2$, t) and dynamically
described by a (reviewed) general relativity theory.
