Cosmology and Dark Matter at the LHC

We examine the question of whether neutralinos produced at the LHC can be shown to be the particles making up the astronomically observed dark matter. If the WIMP alllowed region lies in the SUGRA coannihilation region, then a strong signal for this would be the unexpected near degeneracy of the stau and neutralino i.e., a mass difference \Delta M\simeq (5-15) GeV. For the mSUGRA model we show such a small mass difference can be measured at the LHC using the signal 3\tau+jet+E_T^{\rm miss}. Two observables, opposite sign minus like sign pairs and the peak of the \tau\tau mass distribution allows the simultaneous determination of \Delta M to 15% and the gluino mass M_{\tilde g} to be 6% at the benchmark point of M_{\tilde g}=850 GeV, A_0=0, \mu>0 with 30 fb^{-1}. With 10 fb^{-1}, \Delta M can be determined to 22% and one can probe the parameter space up to m_{1/2}=700 GeV with 100 fb^{-1}.