The derivation of constraints on the mSUGRA parameter space from the entropy of dark matter halos

We derive an expression for the entropy of a present dark matter halo described by a Navarro‐Frenk‐White modified model with a central core. We obtain an expression for the relic abundance of neutralinos by comparing this entropy of the halo with the value it had during the freeze‐out era. Using WMAP observations, we constrain the parameter space for mSUGRA models. Combining our results with the usual abundance criteria, we are able to discriminate clearly among different validity regions for tan β values. For this, we require both criteria to be consistent within a 2σ bound of the WMAP observations for the relic density: 0.112<Ωh2<0.122. We find that for sgn μ = +1, small values of tan β are not favored; only for tan β∼50 are both criteria significantly consistent. Both criteria allow us to put a lower bound on the neutralino mass, mχ⩾141 GeV.