One of the most interesting questions in science is doubtless to find out which is the nature of the matter composing the Universe and a lot of time and effort have been aimed in order to find out an answer to this question. Amazingly, it has not been possible to give a conclusive answer yet. The old belief that matter in Cosmos is made of quarks, leptons and gauge bosons is being abandoned due to the recent observations and the inconsistences which spring out of this supposition. The data are overwhelmingly pointing to the existence of an exotic non baryonic sort of matter which dominates the structure of the Universe at several scales, but its nature remains a puzzle until now. However, the complete identification and accounting of the amounts of the different types of matter and energy which are present in the Universe, is one of the most important achievements of the end of the present cosmology. Recent observations of the luminosity-redshift relation of Ia Supernovae suggest that distant galaxies are moving slower than predicted by Hubble's law, implying an accelerated expansion of the Universe.

The existence of dark matter in the Universe has been firmly established by astronomical observations at very different length-scales, ranging from the neighborhood of the Solar System to clusters of galaxies. The standard way to notice this need for dark matter comes within the framework of mechanics: A large fraction of the mass needed to produce the observed dynamical effects in all these very different systems is not seen. At the galactic scale, the problem is clearly posed: The measurements of rotation curves (tangential velocities of objects) in galaxies show that the coplanar orbital motion of gas in the outer parts of these galaxies keeps a more or less constant velocity up to several luminous radii \cite{persic}. The discrepancy arises when one applies the usual Newtonian dynamics to the observed luminous matter and gas, since then the circular velocity should decrease as one moves outwards. The most widely accepted explanation is that there exists an almost spherical halo of dark matter, its nature being unknown, which surrounds the galaxy and account for the missing mass needed to produce the flat behavior of the rotation curves. This puzzle has stimulated the exploration of several proposals, and very imaginative explanations have been put forward, from exotic matter to non relativistic modifications of Newtonian dynamics \cite{milgrom}. Because the dark matter is such that interacts very weakly with ordinary matter, it is very difficult to detect it by other means than by their gravitational effects on the baryonic matter.

Recently we have proposed the scalar field as a candidate for dark matter in cosmos (see the section of papers). These models consider scalar-tensor theories of gravity where one is able to add mass terms to the total energy density of the space-time. All modern unifying field theories models also contain scalar fields. For example, scalar fields are fundamental fields in the standard model of particles or in Kaluza-Klein and Superstring theories, where scalar fields appear in a natural way after dimensional reduction. In these theories the scalar field could be endowed with a exponential scalar potential. Within this unifying point of view, we show in this letter a possible model for the dark matter in the Universe, supposing that dark matter is of a scalar field nature.