Formation of primordial black holes through Q-balls

We study the primordial black hole (PBH) formation from Q-balls that are non-topological solitons in scalar field theories. We develop a formula for calculating the density perturbations from the Q-ball charge distribution. We also re-examine the condition for the PBH formation in the matter-dominated era and show that the previously derived formula for super-horizon density fluctuations can be applied to the sub-horizon density perturbations. As an example, we consider the Q-balls in the case of gauge-mediated supersymmetry (SUSY) breaking, whose charge distribution was obtained by the lattice simulation. We find that the density perturbations are large enough to produce a significant number of PBHs with mass $10^{-15}\,M_\odot -5\times 10^{-12}\, M_\odot$, which can explain all the dark matter in the universe. In the context of supersymmetry, this mass range corresponds to the SUSY breaking scale $\sim 10^6$ GeV, which is consistent with the SUSY particle masses $\sim 10$ TeV.