We analyze the formation of cosmic structures in models where dark matter is dominated by light gravitinos with a mass of 100 eV – 1 keV, as predicted by gauge-mediated supersymmetry (SUSY) breaking models. After evaluating the number of degrees of freedom at the gravitino decoupling (Formula presented), we compute the transfer function for matter fluctuations and show that gravitinos behave like warm dark matter (WDM) with a free-streaming scale comparable to the galaxy mass scale. We consider different low-density variants of the WDM model, both with and without a cosmological constant, and compare the predictions on the abundances of neutral hydrogen within high-redshift damped Ly-(Formula presented) systems and on the number density of local galaxy clusters with the corresponding observational constraints. We find that none of the models satisfy both constraints at the same time, unless a rather small (Formula presented) value (Formula presented) and a rather large Hubble parameter (Formula presented) is assumed. Furthermore, in a model with warm + hot dark matter, with the hot component provided by massive neutrinos, the strong suppression of fluctuation on scales of (Formula presented) precludes the formation of high-redshift objects, when the low-(Formula presented) cluster abundance is required. We conclude that all different variants of a light gravitino DM dominated model show strong difficulties for what concerns cosmic structure formation. This gives a severe cosmological constraint on the gauge-mediated SUSY breaking scheme.
|Number of pages
|Physical Review D - Particles, Fields, Gravitation and Cosmology
|Published - 1998