  Fundamental theories, like strings, supergravity, Kaluza-Klein, lead after
dimensional reduction and a suitable choice of field configurations, to an
effective action in four dimensions where gravity is coupled non-mininally to
one scalar field, and minimally to another scalar field. These scalar fields
couple non-trivially between themselves. A radiation field is also considered
in this effective action. All the possibilities connected to those fundamental
theories are labeled by two parameters $n$ (related to the non-trivial coupling
of the scalar fields) and $\omega$, connected to the coupling of the
Brans-Dicke like field to gravity. Exact solutions are found, exhibiting a
singulariy-free behaviour, from the four dimensional point of view, for some
values of those parameter. The flatness and horizon problems for these
solutions are also analyzed. It is discussed to which extent the solutions
found are non-singular from the point of view of the original frames. This
reveals to be a much complex problem.

General Relativity and Quantum Cosmology