  Exotic dark matter together with the vacuum energy or cosmological constant
seem to dominate in the Universe. An even higher density of such matter seems
to be gravitationally trapped in the Galaxy. Thus its direct detection is
central to particle physics and cosmology. Current supersymmetric models
provide a natural dark matter candidate which is the lightest supersymmetric
particle (LSP). Such models combined with fairly well understood physics like
the quark substructure of the nucleon and the nuclear structure (form factor
and/or spin response function), permit the evaluation of the event rate for
LSP-nucleus elastic scattering. The thus obtained event rates are, however,
very low or even undetectable. So it is imperative to exploit the modulation
effect, i.e. the dependence of the event rate on the earth's annual motion.
Also it is useful to consider the directional rate, i.e its dependence on the
direction of the recoiling nucleus. In this paper we study such a modulation
effect both in non directional and directional experiments. We calculate both
the differential and the total rates using both isothermal, symmetric as well
as only axially asymmetric, and non isothermal, due to caustic rings, velocity
distributions. We find that in the symmetric case the modulation amplitude is
small. The same is true for the case of caustic rings. The inclusion of
asymmetry, with a realistic enhanced velocity dispersion in the galactocentric
direction, yields an enhanced modulation effect, especially in directional
experiments.
