The Formation of Cosmic Structures in a Light Gravitino Dominated Universe

Abstract

We analyse the formation of cosmic structures in models where the dark matter is dominated by light gravitinos with 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 gravitinos decoupling ($g_{\ast }$), we compute the transfer function for matter fluctuations and show that gravitinos behave like warm dark matter (WDM) with free-streaming scale comparable to the galaxy mass scale. We consider different low-density variants of the WDM model, both with and without cosmological constant, and compare the predictions on the abundances of neutral hydrogen within high-redshift damped Ly--$\alpha$ systems and on the number density of local galaxy clusters with the corresponding observational constraints. We find that none of the models satisfies both constraints at the same time, unless a rather small ${\Omega }_0$ value ($\text{mincir}0.4$) and a rather large Hubble parameter ($\text{magcir}0.9$) is assumed. Furthermore, in a model with warm + hot dark matter, with hot component provided by massive neutrinos, the strong suppression of fluctuation on scales of $\sim 1\text{hm}$ precludes the formation of high-redshift objects, when the low--$z$ 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.

Comments: 28 pages,Latex, submitted for publication to Phys.Rev.D