Solitosynthesis of Q-balls

We study the formation of Q-balls in the early universe, concentrating on potentials with a cubic or quartic attractive interaction. Large Q-balls can form via solitosynthesis, a process of gradual charge accretion, provided some primordial charge assymetry and initial ``seed'' Q-balls exist. We find that such seeds are possible in theories in which the attractive interaction is of the form $A H \psi^* \psi$, with a light ``Higgs'' mass. Condensate formation and fragmentation is only possible for masses $m_\psi$ in the sub-eV range; these Q-balls may survive untill present.