  In this paper we study the general scenario of an effective theory coming
from the compactification of a higher dimensional theory in a string inspired
setting. This leads to gauge coupling unification at an intermediate mass
scale. After having computed all the threshold corrections (due to Kaluza-Klein
modes) to the running of the couplings of the MSSM we embark in a detailed
phenomenological analysis of the model, based on the numerical package
DarkSUSY, to find constraints on the scenario from Dark Matter data. The mass
spectrum of the theory does not have tachyons. Moreover we find that the
neutralino is still the LSP with a relic density compatible with the most
recent experimental data. With respect to the standard mSUGRA scenario we find
that the neutralino is higgsino like in most of the parameter space. Our
modifications to the DarkSUSY package will be shortly available upon request.
