In the Search of Singularity-Free Cosmological Models in Effective Actions

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.