Exotic dark matter together with the vacuum energy (associated with the cosmological constant) seem to dominate the Universe. Thus its direct detection is central to particle physics and cosmology. Supersymmetry provides a natural dark matter candidate, the lightest supersymmetric particle (LSP). One essential ingredient in obtaining the direct detection rates is the density and velocity distribution of the LSP. The detection rate is proportional to this density in our vicinity. Furthermore, since the rates are expected to be very low, one should explore the two characteristic signatures of the process, namely the modulation effect, i.e. the dependence of the event rate on the Earth’s motion and the correlation of the directional rate with the motion of the sun. Both of these crucially depend on the LSP velocity distribution. In the present paper we study simultaneously density profiles and velocity distributions based on the Eddington theory. Subject headings: Cosmology:Eddington theory, velocity profiles, rotational curvesCold Dark Matter:velocity distribution, direct detection rates. Permanent address:Theoretical Physics Division, University of Ioannina, Ioannina, Gr 451 10, Greece. Visiting the Theoretical Physics Division, University of Ioannina, Ioannina, Gr 451 10, Greece.