  The sensitivity of the lightest supersymmetric particle relic density
calculation to different cosmological scenarios is discussed. In particular, we
investigate the effects of modifications of the expansion rate and of the
entropy content in the Early Universe. These effects, even with no
observational consequences, can still drastically modify the relic density
constraints on the SUSY parameter space. We suggest general parametrizations to
evaluate such effects, and derive also constraints from Big-Bang
nucleosynthesis. We show that using the relic density in the context of
supersymmetric constraints requires a clear statement of the underlying
cosmological model assumptions to avoid misinterpretations. On the other hand,
we note that combining the relic density calculation with the eventual future
discoveries at the LHC will hopefully shed light on the Very Early Universe
properties.
