SUSY constraints from relic density: high sensitivity to pre-BBN expansion rate

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.