Q-ball formation in the gravity-mediated SUSY breaking scenario
  We study the formation of Q-balls which are made of flat directions that appear in the supersymmetric extension of the standard model in the context of gravity-mediated supersymmetry breaking. The full non-linear calculations for the dynamics of the complex scalar field are made. Since the scalar potential in this model is flatter than \phi^2, we have found that fluctuations develop and go non-linear to form non-topological solitons, Q-balls. The size of a Q-ball is determined by the most amplified mode, which is completely determined by the model parameters. On the other hand, the charge of Q-balls depends linearly on the initial charge density of the Affleck-Dine (AD) field. Almost all the charges are absorbed into Q-balls, and only a tiny fraction of the charges is carried by a relic AD field. It may lead to some constraints on the baryogenesis and/or parameters in the particle theory. The peculiarity of gravity-mediation is the moving Q-balls. This results in collisions between Q-balls. It may increase the charge of Q-balls, and change its fate. 
S. Kasuya and M. Kawasaki