Topological Defects Formation after Inflation on Lattice Simulation

We consider the formation of topological defects after inflation. In order to take into account the effects of the rescattering of fluctuations, we integrate the classical equation that describes the evolution of a complex scalar field on the two-dimensional lattice with a slab symmetry. The growth of fluctuations during preheating is found not to be enough for defect formation, and rather a long stage of the rescattering of fluctuations after preheating is necessary. We conclude that the topological defects are not formed if the breaking scale \eta is lager than \sim (2 - 3)\times 10^{16} GeV.