  The sensitivity of the lightest supersymmetric particle relic density
calculation to the variation of the cosmological expansion rate before
nucleosynthesis is discussed. We show that such a modification, even extremely
modest and with no consequence on the cosmological observations, can greatly
enhance the calculated relic density, and therefore change the constraints on
the SUSY parameter space drastically. We illustrate this variation in two
examples of SUSY models, and show that it is unsafe to use the lower bound of
the WMAP limits in order to constrain supersymmetry. We therefore suggest to
use only the upper value Omega_DM h^2 < 0.135.
