On the Neutralino as Dark Matter Candidate; 1, Relic Abundance

The neutralino relic abundance is evaluated for a wide range of the neutralino mass, ${\rm 20\ GeV} \leq m_\chi \leq {\rm 1\ TeV}$, by taking into account the full set of final states in the neutralino-neutralino annihilation. The analysis is performed in the Minimal SuSy Standard Model; it is not restricted by stringent GUT assumptions but only constrained by present experimental bounds. We also discuss phenomenological aspects which are employed in the companion paper (II. Direct Detection) where the chances for a successful search for dark matter neutralino are investigated