Gravitino Warm Dark Matter Motivated by the CDF $eeγγ$ Event

The $ee\gamma\gamma +\rlap/E_T$ event observed by the CDF at Fermilab is naturally explained by dynamically supersymmetry breaking models and suggests the presence of the light gravitino which can be a warm dark matter. We consider large scale structure of the universe in the worm dark matter model and find that the warm dark matter plays almost the same role in the formation of the large scale structure as a cold dark matter if its mass is about $0.5$keV. We also study the Ly~$\alpha$ absorption systems which are presumed to be galaxies at high redshifts and show that the baryon density in the damped Ly~$\alpha$ absorption systems predicted by the warm dark matter model is quite consistent with the present observation.