Physical processes taking place in very strong gravitational fields have received much attention in recent years. Many theoretical models of such processes, based on GR as the standard gravitational theory, are troubled by the problem of the appearance of unavoidable singularities. It is well known that the classical description provided by GR is no longer valid when large space-time curvatures do occur (V.P.Frolov, M.A.Markov, e V.F.Mukhanov, Physical Review D 41, 383, 1990). In the attempt to overcome such difficulties, modifications of GR have been proposed, in particular string theories and multidimensional Kaluza-Klein theories. These approaches lead to the Dilaton field theory, in which the strength of a neutral scalar field determines the values of coupling constants in the four-dimensional effective theory. It has been established that this theory is the low-energy limit of string theory, when electromagnetic interactions are present (D.Garfinkle, G.T.Horowitz e A.Strominger, Physical Review D 43, 3140, 1991; G.W.Gibbons e K.Maeda, Nuclear Physics B 298, 741, 1988; J.H.Horne e G.T.Horowitz, Physical Review D 46, 1340, 1992), or also as the result of dimensional reduction of multidimensional Kaluza-Klein theories (R.Sorkin, Physical Review Letters 51, 87, 1983; D.Gross e M.J.Perry, Nuclear Physics B 226, 29, 1983). Afterwards, Dilaton theory was enlarged to include the case of a second scalar field, taken to represent matter interacting with gravity (Z.Tao e X.Xue, Physical Review D 45, 1878, 1992).

The presence of the Dilaton may be seen as a drawback in the formal structure of G R, in the sense that it spoils one of the most beautiful results of this theory: the geometrization of the gravitational interaction. This difficulty can be avoided if the Riemmanian structure of space-time in General Relativity is enlarged. It should be stressed, though, that such generalization is not an arbitrary modification to geometrize the Dilaton field. In fact, it has a distinct and independent motivation put forth by Ehlers et al. (J.Ehlers, F.Pirani e A.Schild, General Relativity, Ed. L.O'Raifeartaigh, Oxford, Clarendon, 1982). These authors sought for an axiomatic formulation to determine the structure of space-time, making use of simple, fundamental elements such as free-falling particles and light rays; the geometrical structure thus obtained was not Riemman?s, but Weyl?s integrable geometry. The latter differs from Riemman geometry by allowing length transportation to become space-time dependent. A scalar (Dilaton) field appears, in this case, as a natural consequence of the assumed fundamental axioms and is assimilated to the affine nature of the new geometry. Its purely geometrical character is thus ensured. Making use of this space-time representation, a theory of gravitation was built in which the gravitational interaction is completely geometrized (M.Novello, L.A.R.Oliveira, J.M.Salim e E.Elbaz, International Journal of Modern Physics D 1, 641, 1993; J.M.Salim e S.L.Sautú, Classical and Quantum Gravity 13, 353, 1996). The presence of this scalar field changes large-scale gravitational processes, and so it requires a new study of some typical gravitational configurations, such as spherically symmetric solutions, both neutral and charged (J.M.Salim e S.L.Sautú, Classical and Quantum Gravity 15, 203, 1998), homogeneous and isotropic cosmological models (H.P.Oliveira, J.M.Salim e S.L.Sautú, Classical and Quantum Gravity 14, 2833, 1998), as well as anisotropic solutions in the presence of magnetic fields (J.M.Salim, S.L.Sautú e R.Martins, Classical and Quantum Gravity 15, 1521, 1998). In many cases, the Dilaton field enables the elimination of singularities that showed up in the corresponding GR solutions, and further provided for the natural generation of inflationary phases in cosmological solutions (J.C.Fabris, J.M.Salim e S.L.Sautú, Modern Physics Letters A 13, 953, 1998).

Next, modifications induced in the background radiation by the presence of the geometrical scalar field will be studied, particularly with regard to the determination of its polarization (M.Zaldarriaga e D.D.Harari, Physical Review D 52, 3276, 1995). An analytical treatment describing cosmic microwave radiation polarization must then be established, taking into account the interaction with the Dilaton field. Furthermore, this study should be enlarged to account for the additional Faraday rotation due to the Dilaton. To do so, both the formalism describing cosmic microwave radiation (M.Giovannini, Physical Review D 56, 3198, 1997) and studies upon Faraday gravitational rotation in the presence of a Dilaton in stationary space-times (M.Nouri-Zonoz, Physical Review D 60, 024013-1, 1999) shall be applied.

In the future, the aim is also to build cosmological models derived from the solutions already obtained (J.C.Fabris, J.M.Salim e S.L.Sautú, Modern Physics Letters A 13, 953, 1998), to compare this models with observational data, and to study the stability of the models and the problem of structure formation. Further cosmological enquiries shall be related to anisotropic models and possible isotropization effects due to or associated to the Dilaton field; in particular, the issue of particle production induced by the Dilaton field and its influence on isotropization.