Can topological defects be formed during preheating?

We study the dynamics of a scalar field $\Phi$ with the potential $g(|\Phi {|}^2-{\eta }^2{)}^2/2\mathrm{}$ $(g$=self-coupling constant, $\eta$=symmetry breaking scale) after inflation and make clear whether topological defects can ever be formed during preheating. In particular, we pay attention to GUT defects $(\eta \simeq {10}^{15}$ $\mathrm{GeV}-{10}^{17}$ $\mathrm{GeV})$, and consider three types of fluctuations. The first one is produced through the parametric resonance, the second is due to the negative curvature of the potential, and the last is created during inflation. We search the parameters $g$ and $\eta$ for which the nonthermal fluctuations of the scalar field do not lead to the defect formation. We find that the GUT defects are not produced after inflation. This fact shows that the positiveness of the effective mass square of the scalar field and the production of large fluctuations whose amplitude is as large as that of homogeneous mode are not enough conditions for full symmetry restoration.