If gravitinos of mass 1 keV (or similar particles) dominate the mass of the universe, a critical scale of galactic size arises due to their collisionless phase mixing. It is shown that density perturbation spectrum of gravitinos is relatively flat between galactic and cluster scales, unlike the massive neutrino case. If gravitinos form the dark matter, initial adiabatic fluctuations lead to a hierarchical picture of clustering. Galaxies form first, but dissipation is necessary for their survival.

• Received 4 December 1981

DOI:https://doi.org/10.1103/PhysRevLett.48.1636