  We study the homogeneous but anisotropic cosmological models of Bianchi in
presence of a massive scalar field using the ADM Hamiltonian formalism. We
begin to describe the main steps to find the ADM Hamiltonian of the General
Relativity with a massive scalar field and then we study the dynamics of the
flat Bianchi type $I$ anisotropic Universe according to initial and final
values of this Hamiltonian and sign of the potential. After a brief recall of
the conditions necessary to isotropise an anisotropic Bianchi class A model
with such a field, we extend them to a non minimally coupled scalar field by
using a conformal transformation of the metric which casts the General
Relativity with a scalar field into a scalar-tensor theory. The new line
element then corresponds to the so-called Brans-Dicke frame, the former one
being the Einstein frame. Then, we study the isotropisation process of the
Bianchi class A model when we consider the low energy form of the string theory
without its antisymmetric tensor and the Brans-Dicke theory with some
exponential or power laws of the scalar field for the potential. Finally,
assuming an isotropic Universe such as all the metric functions behave as some
power or exponential laws of the proper time, we find the conditions such that
the gravitation function and the potential of the scalar field are bounded as
it is observed today, and compare them with the necessary conditions for
isotropy.
